K3 Surfaces

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Lectures on K3 Surfaces

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1316797252
Total Pages : 499 pages
Book Rating : 4.3/5 (167 download)

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Book Synopsis Lectures on K3 Surfaces by : Daniel Huybrechts

Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

K3 Surfaces

Author : Shigeyuki Kondō
Publisher :
ISBN 13 : 9783037197080
Total Pages : 250 pages
Book Rating : 4.1/5 (97 download)

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Book Synopsis K3 Surfaces by : Shigeyuki Kondō

Download or read book K3 Surfaces written by Shigeyuki Kondō and published by . This book was released on 2020 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: $K3$ surfaces are a key piece in the classification of complex analytic or algebraic surfaces. The term was coined by A. Weil in 1958 - a result of the initials Kummer, Kähler, Kodaira, and the mountain K2 found in Karakoram. The most famous example is the Kummer surface discovered in the 19th century.$K3$ surfaces can be considered as a 2-dimensional analogue of an elliptic curve, and the theory of periods - called the Torelli-type theorem for $K3$ surfaces - was established around 1970. Since then, several pieces of research on $K3$ surfaces have been undertaken and more recently $K3$ surfaces have even become of interest in theoretical physics.The main purpose of this book is an introduction to the Torelli-type theorem for complex analytic $K3$ surfaces, and its applications. The theory of lattices and their reflection groups is necessary to study $K3$ surfaces, and this book introduces these notions. The book contains, as well as lattices and reflection groups, the classification of complex analytic surfaces, the Torelli-type theorem, the subjectivity of the period map, Enriques surfaces, an application to the moduli space of plane quartics, finite automorphisms of $K3$ surfaces, Niemeier lattices and the Mathieu group, the automorphism group of Kummer surfaces and the Leech lattice.The author seeks to demonstrate the interplay between several sorts of mathematics and hopes the book will prove helpful to researchers in algebraic geometry and related areas, and to graduate students with a basic grounding in algebraic geometry.

K3 Surfaces and Their Moduli

Author : Carel Faber
Publisher : Birkhäuser
ISBN 13 : 331929959X
Total Pages : 399 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis K3 Surfaces and Their Moduli by : Carel Faber

Download or read book K3 Surfaces and Their Moduli written by Carel Faber and published by Birkhäuser. This book was released on 2016-04-22 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties,” which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics. K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both mathematicians and theoretical physicists. Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significant impetus due to recent breakthroughs on the Tate conjecture, the study of stability conditions and derived categories, and links with mirror symmetry and string theory. At the same time, the theory of irreducible holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has become a mainstream topic in algebraic geometry. Contributors: S. Boissière, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M. Nieper-Wisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.

Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds

Author : Radu Laza
Publisher : Springer Science & Business Media
ISBN 13 : 146146403X
Total Pages : 613 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds by : Radu Laza

Download or read book Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds written by Radu Laza and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.

Complex Analysis and Algebraic Geometry

Author : Kunihiko Kodaira
Publisher : CUP Archive
ISBN 13 : 9780521217774
Total Pages : 424 pages
Book Rating : 4.2/5 (177 download)

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Book Synopsis Complex Analysis and Algebraic Geometry by : Kunihiko Kodaira

Download or read book Complex Analysis and Algebraic Geometry written by Kunihiko Kodaira and published by CUP Archive. This book was released on 1977 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.

Lectures on K3 Surfaces

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1107153042
Total Pages : 499 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Lectures on K3 Surfaces by : Daniel Huybrechts

Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

Algebraic Geometry III

Author : A.N. Parshin
Publisher : Springer Science & Business Media
ISBN 13 : 9783540546818
Total Pages : 290 pages
Book Rating : 4.5/5 (468 download)

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Book Synopsis Algebraic Geometry III by : A.N. Parshin

Download or read book Algebraic Geometry III written by A.N. Parshin and published by Springer Science & Business Media. This book was released on 1997-12-08 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.

Complex Analysis and Geometry

Author : Vincenzo Ancona
Publisher : CRC Press
ISBN 13 : 9780582292765
Total Pages : 204 pages
Book Rating : 4.2/5 (927 download)

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Book Synopsis Complex Analysis and Geometry by : Vincenzo Ancona

Download or read book Complex Analysis and Geometry written by Vincenzo Ancona and published by CRC Press. This book was released on 1997-04-27 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on two conferences held in Trento, Italy, this volume contains 13 research papers and two survey papers on complex analysis and complex algebraic geometry. The main topics addressed by these leading researchers include: Mori theory polynomial hull vector bundles q-convexity Lie groups and actions on complex spaces hypercomplex structures pseudoconvex domains projective varieties Peer-reviewed and extensively referenced, Complex Analysis and Geometry contains recent advances and important research results. It also details several problems that remain open, the resolution of which could further advance the field.

Real Enriques Surfaces

Author : Alexander Degtyarev
Publisher : Springer
ISBN 13 : 3540399488
Total Pages : 275 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Real Enriques Surfaces by : Alexander Degtyarev

Download or read book Real Enriques Surfaces written by Alexander Degtyarev and published by Springer. This book was released on 2007-05-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up to deformation. Simple explicit topological invariants are elaborated for identifying the deformation classes of real Enriques surfaces. Some of theses are new and can be applied to other classes of surfaces or higher-dimensional varieties. Intended for researchers and graduate students in real algebraic geometry it may also interest others who want to become familiar with the field and its techniques. The study relies on topology of involutions, arithmetics of integral quadratic forms, algebraic geometry of surfaces, and the hyperkähler structure of K3-surfaces. A comprehensive summary of the necessary results and techniques from each of these fields is included. Some results are developed further, e.g., a detailed study of lattices with a pair of commuting involutions and a certain class of rational complex surfaces.

Fourier-Mukai Transforms in Algebraic Geometry

Author : Daniel Huybrechts
Publisher : Oxford University Press on Demand
ISBN 13 : 0199296863
Total Pages : 316 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Fourier-Mukai Transforms in Algebraic Geometry by : Daniel Huybrechts

Download or read book Fourier-Mukai Transforms in Algebraic Geometry written by Daniel Huybrechts and published by Oxford University Press on Demand. This book was released on 2006-04-20 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is based on a course given at the Institut de Mathematiques de Jussieu, on the derived category of coherent sheaves on a smooth projective variety. It is aimed at students with a basic knowledge of algebraic geometry and contains full proofs and exercises that aid the reader.

Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces

Author : Maurizio Cornalba
Publisher : World Scientific
ISBN 13 : 9814590878
Total Pages : 716 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces by : Maurizio Cornalba

Download or read book Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces written by Maurizio Cornalba and published by World Scientific. This book was released on 1989-06-01 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Picard Lattices of Families of K3 Surfaces

Author : Sarah-Marie Belcastro
Publisher :
ISBN 13 :
Total Pages : 378 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Picard Lattices of Families of K3 Surfaces by : Sarah-Marie Belcastro

Download or read book Picard Lattices of Families of K3 Surfaces written by Sarah-Marie Belcastro and published by . This book was released on 1997 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Birational Geometry, Rational Curves, and Arithmetic

Author : Fedor Bogomolov
Publisher : Springer Science & Business Media
ISBN 13 : 146146482X
Total Pages : 324 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Birational Geometry, Rational Curves, and Arithmetic by : Fedor Bogomolov

Download or read book Birational Geometry, Rational Curves, and Arithmetic written by Fedor Bogomolov and published by Springer Science & Business Media. This book was released on 2013-05-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

Compact Complex Surfaces

Author : W. Barth
Publisher : Springer Science & Business Media
ISBN 13 : 364296754X
Total Pages : 315 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Compact Complex Surfaces by : W. Barth

Download or read book Compact Complex Surfaces written by W. Barth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Introduction. - Standard Notations. - Preliminaries. - Curves on Surfaces. - Mappings of Surfaces. - Some General Properties of Surfaces. - Examples. - The Enriques-Kodaira Classification. - Surfaces of General Type. - K3-Surfaces and Enriques Surfaces. - Bibliography. - Subject Index.

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

Author : Martin Schlichenmaier
Publisher : Springer Science & Business Media
ISBN 13 : 3540711759
Total Pages : 217 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces by : Martin Schlichenmaier

Download or read book An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces written by Martin Schlichenmaier and published by Springer Science & Business Media. This book was released on 2010-02-11 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.

Number Theory

Author : Canadian Number Theory Association. Conference
Publisher : American Mathematical Soc.
ISBN 13 : 9780821803127
Total Pages : 460 pages
Book Rating : 4.8/5 (31 download)

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Book Synopsis Number Theory by : Canadian Number Theory Association. Conference

Download or read book Number Theory written by Canadian Number Theory Association. Conference and published by American Mathematical Soc.. This book was released on 1995 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains proceedings presented at the fourth Canadian Number Theory Association conference held at Dalhousie University in July 1994. The invited speakers focused on analytic, algebraic, and computational number theory. The contributed talks represented a wide variety of areas in number theory.

Mirror Symmetry II

Author : Brian Greene
Publisher : American Mathematical Soc.
ISBN 13 : 0821827448
Total Pages : 862 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mirror Symmetry II by : Brian Greene

Download or read book Mirror Symmetry II written by Brian Greene and published by American Mathematical Soc.. This book was released on 1997 with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mirror Symmetry has undergone dramatic progress since the Mathematical Sciences Research Institute (MSRI) workshop in 1991, whose proceedings constitute voluem I of this continuing collection. Tremendous insight has been gained on a number of key issues. This volume surveys these results. Some of the contributions in this work have appeared elsewhere, while others were written specifically for this collection. The areas covered are organized into 4 sections, and each presents papers by both physicists and mathematicians. This volume collects the most important developments that have taken place in mathematical physics since 1991. It is an essential reference tool for both mathematics and physics libraries and for students of physics and mathematics. Titles in this series are co-published, between the American Mathematical Society and International Press, Cambridge, MA, USA.