Moduli Of K Stable Varieties

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Moduli of K-stable Varieties

Author : Giulio Codogni
Publisher : Springer
ISBN 13 : 3030131580
Total Pages : 181 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Moduli of K-stable Varieties by : Giulio Codogni

Download or read book Moduli of K-stable Varieties written by Giulio Codogni and published by Springer. This book was released on 2019-06-27 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outcome of the workshop "Moduli of K-stable Varieties", which was held in Rome, Italy in 2017. The content focuses on the existence problem for canonical Kähler metrics and links to the algebro-geometric notion of K-stability. The book includes both surveys on this problem, notably in the case of Fano varieties, and original contributions addressing this and related problems. The papers in the latter group develop the theory of K-stability; explore canonical metrics in the Kähler and almost-Kähler settings; offer new insights into the geometric significance of K-stability; and develop tropical aspects of the moduli space of curves, the singularity theory necessary for higher dimensional moduli theory, and the existence of minimal models. Reflecting the advances made in the area in recent years, the survey articles provide an essential overview of many of the most important findings. The book is intended for all advanced graduate students and researchers who want to learn about recent developments in the theory of moduli space, K-stability and Kähler-Einstein metrics.

Moduli of K-stable Varieties

Author : Giulio Codogni
Publisher :
ISBN 13 : 9783030131593
Total Pages : 181 pages
Book Rating : 4.1/5 (315 download)

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Book Synopsis Moduli of K-stable Varieties by : Giulio Codogni

Download or read book Moduli of K-stable Varieties written by Giulio Codogni and published by . This book was released on 2019 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outcome of the workshop "Moduli of K-stable Varieties", which was held in Rome, Italy in 2017. The content focuses on the existence problem for canonical Kèahler metrics and links to the algebro-geometric notion of K-stability. The book includes both surveys on this problem, notably in the case of Fano varieties, and original contributions addressing this and related problems. The papers in the latter group develop the theory of K-stability; explore canonical metrics in the Kèahler and almost-Kèahler settings; offer new insights into the geometric significance of K-stability; and develop tropical aspects of the moduli space of curves, the singularity theory necessary for higher dimensional moduli theory, and the existence of minimal models. Reflecting the advances made in the area in recent years, the survey articles provide an essential overview of many of the most important findings. The book is intended for all advanced graduate students and researchers who want to learn about recent developments in the theory of moduli space, K-stability and Kèahler-Einstein metrics.

Families of Varieties of General Type

Author : János Kollár
Publisher : Cambridge University Press
ISBN 13 : 1009346105
Total Pages : 491 pages
Book Rating : 4.0/5 (93 download)

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Book Synopsis Families of Varieties of General Type by : János Kollár

Download or read book Families of Varieties of General Type written by János Kollár and published by Cambridge University Press. This book was released on 2023-04-30 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.

Birational Geometry, Kähler–Einstein Metrics and Degenerations

Author : Ivan Cheltsov
Publisher : Springer Nature
ISBN 13 : 3031178599
Total Pages : 882 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Birational Geometry, Kähler–Einstein Metrics and Degenerations by : Ivan Cheltsov

Download or read book Birational Geometry, Kähler–Einstein Metrics and Degenerations written by Ivan Cheltsov and published by Springer Nature. This book was released on 2023-05-23 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and Pohang The conferences were focused on the following two related problems: • existence of Kähler–Einstein metrics on Fano varieties • degenerations of Fano varieties on which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide. These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.

Moduli Theory and Classification Theory of Algebraic Varieties

Author : H. Popp
Publisher : Springer
ISBN 13 : 3540370315
Total Pages : 196 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Moduli Theory and Classification Theory of Algebraic Varieties by : H. Popp

Download or read book Moduli Theory and Classification Theory of Algebraic Varieties written by H. Popp and published by Springer. This book was released on 2006-11-15 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modern Geometry: A Celebration of the Work of Simon Donaldson

Author : Vicente Muñoz
Publisher : American Mathematical Soc.
ISBN 13 : 1470440946
Total Pages : 416 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Modern Geometry: A Celebration of the Work of Simon Donaldson by : Vicente Muñoz

Download or read book Modern Geometry: A Celebration of the Work of Simon Donaldson written by Vicente Muñoz and published by American Mathematical Soc.. This book was released on 2018-09-05 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of survey articles of exciting new developments in geometry, written in tribute to Simon Donaldson to celebrate his 60th birthday. Reflecting the wide range of Donaldson's interests and influence, the papers range from algebraic geometry and topology through symplectic geometry and geometric analysis to mathematical physics. Their expository nature means the book acts as an invitation to the various topics described, while also giving a sense of the links between these different areas and the unity of modern geometry.

Complex and Symplectic Geometry

Author : Daniele Angella
Publisher : Springer
ISBN 13 : 331962914X
Total Pages : 262 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Complex and Symplectic Geometry by : Daniele Angella

Download or read book Complex and Symplectic Geometry written by Daniele Angella and published by Springer. This book was released on 2017-10-12 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Stacks Project Expository Collection

Author : Pieter Belmans
Publisher : Cambridge University Press
ISBN 13 : 1009063286
Total Pages : 308 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Stacks Project Expository Collection by : Pieter Belmans

Download or read book Stacks Project Expository Collection written by Pieter Belmans and published by Cambridge University Press. This book was released on 2022-09-30 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne–Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces.

Algebraic Geometry: Salt Lake City 2015 (Part 1)

Author : Tommaso de Fernex
Publisher : American Mathematical Soc.
ISBN 13 : 1470435772
Total Pages : 655 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Geometry: Salt Lake City 2015 (Part 1) by : Tommaso de Fernex

Download or read book Algebraic Geometry: Salt Lake City 2015 (Part 1) written by Tommaso de Fernex and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.

Geometric Analysis

Author : Jingyi Chen
Publisher : Springer Nature
ISBN 13 : 3030349535
Total Pages : 616 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Geometric Analysis by : Jingyi Chen

Download or read book Geometric Analysis written by Jingyi Chen and published by Springer Nature. This book was released on 2020-04-10 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Sławomir Kołodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Rivière, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author : Sirakov Boyan
Publisher : World Scientific
ISBN 13 : 9813272899
Total Pages : 5396 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Sirakov Boyan

Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Theory of Algebraic Surfaces

Author : Kunihiko Kodaira
Publisher : Springer Nature
ISBN 13 : 9811573808
Total Pages : 86 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Theory of Algebraic Surfaces by : Kunihiko Kodaira

Download or read book Theory of Algebraic Surfaces written by Kunihiko Kodaira and published by Springer Nature. This book was released on 2020-09-17 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an English translation of the book in Japanese, published as the volume 20 in the series of Seminar Notes from The University of Tokyo that grew out of a course of lectures by Professor Kunihiko Kodaira in 1967. It serves as an almost self-contained introduction to the theory of complex algebraic surfaces, including concise proofs of Gorenstein's theorem for curves on a surface and Noether's formula for the arithmetic genus. It also discusses the behavior of the pluri-canonical maps of surfaces of general type as a practical application of the general theory. The book is aimed at graduate students and also at anyone interested in algebraic surfaces, and readers are expected to have only a basic knowledge of complex manifolds as a prerequisite.

The Geometry of Moduli Spaces of Sheaves

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1139485822
Total Pages : 345 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts

Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Tropical and Non-Archimedean Geometry

Author : Omid Amini
Publisher : American Mathematical Soc.
ISBN 13 : 1470410214
Total Pages : 274 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Tropical and Non-Archimedean Geometry by : Omid Amini

Download or read book Tropical and Non-Archimedean Geometry written by Omid Amini and published by American Mathematical Soc.. This book was released on 2014-12-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past decade, it has become apparent that tropical geometry and non-Archimedean geometry should be studied in tandem; each subject has a great deal to say about the other. This volume is a collection of articles dedicated to one or both of these disciplines. Some of the articles are based, at least in part, on the authors' lectures at the 2011 Bellairs Workshop in Number Theory, held from May 6-13, 2011, at the Bellairs Research Institute, Holetown, Barbados. Lecture topics covered in this volume include polyhedral structures on tropical varieties, the structure theory of non-Archimedean curves (algebraic, analytic, tropical, and formal), uniformisation theory for non-Archimedean curves and abelian varieties, and applications to Diophantine geometry. Additional articles selected for inclusion in this volume represent other facets of current research and illuminate connections between tropical geometry, non-Archimedean geometry, toric geometry, algebraic graph theory, and algorithmic aspects of systems of polynomial equations.

Iitaka Conjecture

Author : Osamu Fujino
Publisher : Springer Nature
ISBN 13 : 9811533474
Total Pages : 138 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Iitaka Conjecture by : Osamu Fujino

Download or read book Iitaka Conjecture written by Osamu Fujino and published by Springer Nature. This book was released on 2020-04-09 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ambitious program for the birational classification of higher-dimensional complex algebraic varieties initiated by Shigeru Iitaka around 1970 is usually called the Iitaka program. Now it is known that the heart of the Iitaka program is the Iitaka conjecture, which claims the subadditivity of the Kodaira dimension for fiber spaces. The main purpose of this book is to make the Iitaka conjecture more accessible. First, Viehweg's theory of weakly positive sheaves and big sheaves is described, and it is shown that the Iitaka conjecture follows from the Viehweg conjecture. Then, the Iitaka conjecture is proved in some special and interesting cases. A relatively simple new proof of Viehweg's conjecture is given for fiber spaces whose geometric generic fiber is of general type based on the weak semistable reduction theorem due to Abramovick–Karu and the existence theorem of relative canonical models by Birkar–Cascini–Hacon–McKernan. No deep results of the theory of variations of Hodge structure are needed. The Iitaka conjecture for fiber spaces whose base space is of general type is also proved as an easy application of Viehweg's weak positivity theorem, and the Viehweg conjecture for fiber spaces whose general fibers are elliptic curves is explained. Finally, the subadditivity of the logarithmic Kodaira dimension for morphisms of relative dimension one is proved. In this book, for the reader's convenience, known arguments as well as some results are simplified and generalized with the aid of relatively new techniques.

Resolution of Singularities

Author : Herwig Hauser
Publisher : Birkhäuser
ISBN 13 : 3034883994
Total Pages : 610 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Resolution of Singularities by : Herwig Hauser

Download or read book Resolution of Singularities written by Herwig Hauser and published by Birkhäuser. This book was released on 2012-12-06 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: In September 1997, the Working Week on Resolution of Singularities was held at Obergurgl in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up part I of this volume. They are complemented in part II by fifteen selected contributions on specific topics and resolution theories. The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems.

Algebraic Geometry

Author : Richard Thomas
Publisher : American Mathematical Soc.
ISBN 13 : 1470435780
Total Pages : 635 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Geometry by : Richard Thomas

Download or read book Algebraic Geometry written by Richard Thomas and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Part 2 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.