Grassmannians Moduli Spaces And Vector Bundles

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Grassmannians, Moduli Spaces and Vector Bundles

Author : David Ellwood
Publisher : American Mathematical Soc.
ISBN 13 : 0821852051
Total Pages : 190 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Grassmannians, Moduli Spaces and Vector Bundles by : David Ellwood

Download or read book Grassmannians, Moduli Spaces and Vector Bundles written by David Ellwood and published by American Mathematical Soc.. This book was released on 2011 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of cutting-edge articles on vector bundles and related topics originated from a CMI workshop, held in October 2006, that brought together a community indebted to the pioneering work of P. E. Newstead, visiting the United States for the first time since the 1960s. Moduli spaces of vector bundles were then in their infancy, but are now, as demonstrated by this volume, a powerful tool in symplectic geometry, number theory, mathematical physics, and algebraic geometry. In fact, the impetus for this volume was to offer a sample of the vital convergence of techniques and fundamental progress, taking place in moduli spaces at the outset of the twenty-first century. This volume contains contributions by J. E. Andersen and N. L. Gammelgaard (Hitchin's projectively flat connection and Toeplitz operators), M. Aprodu and G. Farkas (moduli spaces), D. Arcara and A. Bertram (stability in higher dimension), L. Jeffrey (intersection cohomology), J. Kamnitzer (Langlands program), M. Lieblich (arithmetic aspects), P. E. Newstead (coherent systems), G. Pareschi and M. Popa (linear series on Abelian varieties), and M. Teixidor i Bigas (bundles over reducible curves). These articles do require a working knowledge of algebraic geometry, symplectic geometry and functional analysis, but should appeal to practitioners in a diversity of fields. No specialization should be necessary to appreciate the contributions, or possibly to be stimulated to work in the various directions opened by these path-blazing ideas; to mention a few, the Langlands program, stability criteria for vector bundles over surfaces and threefolds, linear series over abelian varieties and Brauer groups in relation to arithmetic properties of moduli spaces.

Grassmannians, Moduli Spaces and Vector Bundles

Author : David Ellwood
Publisher :
ISBN 13 : 9787040510393
Total Pages : 180 pages
Book Rating : 4.5/5 (13 download)

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Book Synopsis Grassmannians, Moduli Spaces and Vector Bundles by : David Ellwood

Download or read book Grassmannians, Moduli Spaces and Vector Bundles written by David Ellwood and published by . This book was released on 2019 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Moduli Spaces and Vector Bundles

Author : Leticia Brambila-Paz
Publisher : Cambridge University Press
ISBN 13 : 1139480049
Total Pages : 506 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Moduli Spaces and Vector Bundles by : Leticia Brambila-Paz

Download or read book Moduli Spaces and Vector Bundles written by Leticia Brambila-Paz and published by Cambridge University Press. This book was released on 2009-05-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory. Peter E. Newstead has been a leading figure in this field almost from its inception and has made many seminal contributions to our understanding of moduli spaces of stable bundles. This volume has been assembled in tribute to Professor Newstead and his contribution to algebraic geometry. Some of the subject's leading experts cover foundational material, while the survey and research papers focus on topics at the forefront of the field. This volume is suitable for both graduate students and more experienced researchers.

Moduli Spaces and Vector Bundles—New Trends

Author : Peter Gothen
Publisher : American Mathematical Society
ISBN 13 : 1470472961
Total Pages : 382 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Moduli Spaces and Vector Bundles—New Trends by : Peter Gothen

Download or read book Moduli Spaces and Vector Bundles—New Trends written by Peter Gothen and published by American Mathematical Society. This book was released on 2024-07-18 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the VBAC 2022 Conference on Moduli Spaces and Vector Bundles—New Trends, held in honor of Peter Newstead's 80th birthday, from July 25–29, 2022, at the University of Warwick, Coventry, United Kingdom. The papers focus on the theory of stability conditions in derived categories, non-reductive geometric invariant theory, Brill-Noether theory, and Higgs bundles and character varieties. The volume includes both survey and original research articles. Most articles contain substantial background and will be helpful to both novices and experts.

Moduli of Vector Bundles

Author : Masaki Maruyama
Publisher : CRC Press
ISBN 13 : 1000950700
Total Pages : 324 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Moduli of Vector Bundles by : Masaki Maruyama

Download or read book Moduli of Vector Bundles written by Masaki Maruyama and published by CRC Press. This book was released on 2023-05-31 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains papers presented at the 35th Taniguchi International Symposium held recently in Sanda and Kyoto, Japan. Details the latest developments concerning moduli spaces of vector bundles or instantons and their application. Covers a broad array of topics in both differential and algebraic geometry."

Compact Moduli Spaces and Vector Bundles

Author : Valery Alexeev
Publisher : American Mathematical Soc.
ISBN 13 : 0821868993
Total Pages : 264 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Compact Moduli Spaces and Vector Bundles by : Valery Alexeev

Download or read book Compact Moduli Spaces and Vector Bundles written by Valery Alexeev and published by American Mathematical Soc.. This book was released on 2012 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the conference on Compact Moduli and Vector Bundles, held from October 21-24, 2010, at the University of Georgia. This book is a mix of survey papers and original research articles on two related subjects: Compact Moduli spaces of algebraic varieties, including of higher-dimensional stable varieties and pairs, and Vector Bundles on such compact moduli spaces, including the conformal block bundles. These bundles originated in the 1970s in physics; the celebrated Verlinde formula computes their ranks. Among the surveys are those that examine compact moduli spaces of surfaces of general type and others that concern the GIT constructions of log canonical models of moduli of stable curves. The original research articles include, among others, papers on a formula for the Chern classes of conformal classes of conformal block bundles on the moduli spaces of stable curves, on Looijenga's conjectures, on algebraic and tropical Brill-Noether theory, on Green's conjecture, on rigid curves on moduli of curves, and on Steiner surfaces.

Cohomology of Vector Bundles and Syzygies

Author : Jerzy Weyman
Publisher : Cambridge University Press
ISBN 13 : 9780521621977
Total Pages : 404 pages
Book Rating : 4.6/5 (219 download)

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Book Synopsis Cohomology of Vector Bundles and Syzygies by : Jerzy Weyman

Download or read book Cohomology of Vector Bundles and Syzygies written by Jerzy Weyman and published by Cambridge University Press. This book was released on 2003-06-09 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.

The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles

Author : Richard Wentworth
Publisher : World Scientific
ISBN 13 : 9813229101
Total Pages : 412 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles by : Richard Wentworth

Download or read book The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles written by Richard Wentworth and published by World Scientific. This book was released on 2018-06-28 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngô Bau Châu's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field.

An Introduction to Invariants and Moduli

Author : Shigeru Mukai
Publisher : Cambridge University Press
ISBN 13 : 9780521809061
Total Pages : 528 pages
Book Rating : 4.8/5 (9 download)

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Book Synopsis An Introduction to Invariants and Moduli by : Shigeru Mukai

Download or read book An Introduction to Invariants and Moduli written by Shigeru Mukai and published by Cambridge University Press. This book was released on 2003-09-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample Text

Recent Advances in Algebraic Geometry

Author : Christopher D. Hacon
Publisher : Cambridge University Press
ISBN 13 : 110764755X
Total Pages : 451 pages
Book Rating : 4.1/5 (76 download)

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Book Synopsis Recent Advances in Algebraic Geometry by : Christopher D. Hacon

Download or read book Recent Advances in Algebraic Geometry written by Christopher D. Hacon and published by Cambridge University Press. This book was released on 2015-01-15 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

Conformal Blocks, Generalized Theta Functions and the Verlinde Formula

Author : Shrawan Kumar
Publisher : Cambridge University Press
ISBN 13 : 1009002872
Total Pages : 540 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Conformal Blocks, Generalized Theta Functions and the Verlinde Formula by : Shrawan Kumar

Download or read book Conformal Blocks, Generalized Theta Functions and the Verlinde Formula written by Shrawan Kumar and published by Cambridge University Press. This book was released on 2021-11-25 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics.

Algebraic Geometry: Salt Lake City 2015

Author : Tommaso de Fernex
Publisher : American Mathematical Soc.
ISBN 13 : 1470435772
Total Pages : 674 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Geometry: Salt Lake City 2015 by : Tommaso de Fernex

Download or read book Algebraic Geometry: Salt Lake City 2015 written by Tommaso de Fernex and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 674 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.

Integrable Systems and Algebraic Geometry: Volume 1

Author : Ron Donagi
Publisher : Cambridge University Press
ISBN 13 : 110880358X
Total Pages : 421 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Integrable Systems and Algebraic Geometry: Volume 1 by : Ron Donagi

Download or read book Integrable Systems and Algebraic Geometry: Volume 1 written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-04-02 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.

Integrable Systems and Algebraic Geometry

Author : Ron Donagi
Publisher : Cambridge University Press
ISBN 13 : 1108715745
Total Pages : 421 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis Integrable Systems and Algebraic Geometry by : Ron Donagi

Download or read book Integrable Systems and Algebraic Geometry written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-04-02 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Geometry of Moduli

Author : Jan Arthur Christophersen
Publisher : Springer
ISBN 13 : 3319948814
Total Pages : 330 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Geometry of Moduli by : Jan Arthur Christophersen

Download or read book Geometry of Moduli written by Jan Arthur Christophersen and published by Springer. This book was released on 2018-11-24 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in which moduli theory is advancing. These include the geometry of moduli spaces, non-reductive geometric invariant theory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies of curves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.

Integrable Systems and Algebraic Geometry: Volume 2

Author : Ron Donagi
Publisher : Cambridge University Press
ISBN 13 : 1108805337
Total Pages : 537 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Integrable Systems and Algebraic Geometry: Volume 2 by : Ron Donagi

Download or read book Integrable Systems and Algebraic Geometry: Volume 2 written by Ron Donagi and published by Cambridge University Press. This book was released on 2020-04-02 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Created as a celebration of mathematical pioneer Emma Previato, this comprehensive second volume highlights the connections between her main fields of research, namely algebraic geometry and integrable systems. Written by leaders in the field, the text is accessible to graduate students and non-experts, as well as researchers.

Local and Global Methods in Algebraic Geometry

Author : Nero Budur
Publisher : American Mathematical Soc.
ISBN 13 : 1470434881
Total Pages : 370 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Local and Global Methods in Algebraic Geometry by : Nero Budur

Download or read book Local and Global Methods in Algebraic Geometry written by Nero Budur and published by American Mathematical Soc.. This book was released on 2018-07-26 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Local and Global Methods in Algebraic Geometry, held from May 12–15, 2016, at the University of Illinois at Chicago, in honor of Lawrence Ein's 60th birthday. The articles cover a broad range of topics in algebraic geometry and related fields, including birational geometry and moduli theory, analytic and positive characteristic methods, geometry of surfaces, singularity theory, hyper-Kähler geometry, rational points, and rational curves.