Moduli Spaces
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Geometry Of Moduli Spaces And Representation Theory
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Author : Roman Bezrukavnikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-15
Geometry Of Moduli Spaces And Representation Theory written by Roman Bezrukavnikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Mathematics categories.
This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program “Geometry of moduli spaces and representation theory”, and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory. Geometric representation theory is a young but fast developing research area at the intersection of these subjects. An early profound achievement was the famous conjecture by Kazhdan–Lusztig about characters of highest weight modules over a complex semi-simple Lie algebra, and its subsequent proof by Beilinson-Bernstein and Brylinski-Kashiwara. Two remarkable features of this proof have inspired much of subsequent development: intricate algebraic data turned out to be encoded in topological invariants of singular geometric spaces, while proving this fact required deep general theorems from algebraic geometry. Another focus of the program was enumerative algebraic geometry. Recent progress showed the role of Lie theoretic structures in problems such as calculation of quantum cohomology, K-theory, etc. Although the motivation and technical background of these constructions is quite different from that of geometric Langlands duality, both theories deal with topological invariants of moduli spaces of maps from a target of complex dimension one. Thus they are at least heuristically related, while several recent works indicate possible strong technical connections. The main goal of this collection of notes is to provide young researchers and experts alike with an introduction to these areas of active research and promote interaction between the two related directions.
The Moduli Space Of Curves
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Author : R. Dijkgraaf
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-10-18
The Moduli Space Of Curves written by R. Dijkgraaf and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-18 with Mathematics categories.
The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory. Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science." Witteen’s conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory.
The Geometry Of Moduli Spaces Of Sheaves
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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-27
The Geometry Of Moduli Spaces Of Sheaves written by Daniel Huybrechts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-27 with Mathematics categories.
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.
Moduli Spaces And Vector Bundles
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Author : Steve Bradlow
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-21
Moduli Spaces And Vector Bundles written by Steve Bradlow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-21 with Mathematics categories.
Coverage includes foundational material as well as current research, authored by top specialists within their fields.
Moduli Spaces Of Riemann Surfaces
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Author : Benson Farb
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-16
Moduli Spaces Of Riemann Surfaces written by Benson Farb and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-16 with Mathematics categories.
Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Compactifying Moduli Spaces For Abelian Varieties
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Author : Martin C. Olsson
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-25
Compactifying Moduli Spaces For Abelian Varieties written by Martin C. Olsson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-25 with Mathematics categories.
This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.
Algebraic Curves
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Author : Maxim E. Kazaryan
language : en
Publisher: Springer
Release Date : 2019-01-21
Algebraic Curves written by Maxim E. Kazaryan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-21 with Mathematics categories.
This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework
Moduli Spaces
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Author : Leticia Brambila
language : en
Publisher: Cambridge University Press
Release Date : 2014-03-13
Moduli Spaces written by Leticia Brambila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-13 with Mathematics categories.
A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.
Moduli Spaces Of Curves Mapping Class Groups And Field Theory
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Author : Xavier Buff
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Moduli Spaces Of Curves Mapping Class Groups And Field Theory written by Xavier Buff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
It concludes with a study of the canonical Galois action on the fundamental groupoids, computed using Grothendick-Teichmuller theory. Finally, Chapter 3 studies strict ribbon categories, which are closely related to braided tensor categories: here they are used to construct invariants of 3-manifolds which in turn give rise to quantum field theories."--BOOK JACKET.
Moduli Of Curves
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Author : Joe Harris
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
Moduli Of Curves written by Joe Harris and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.
The aim of this book is to provide a guide to a rich and fascinating subject: algebraic curves, and how they vary in families. The revolution that the field of algebraic geometry has undergone with the introduction of schemes, together with new ideas, techniques and viewpoints introduced by Mumford and others, have made it possible for us to understand the behavior of curves in ways that simply were not possible a half-century ago. This in turn has led, over the last few decades, to a burst of activity in the area, resolving longstanding problems and generating new and unforeseen results and questions. We hope to acquaint you both with these results and with the ideas that have made them possible. The book isn’t intended to be a definitive reference: the subject is developing too rapidly for that to be a feasible goal, even if we had the expertise necessary for the task. Our preference has been to focus on examples and applications rather than on foundations. When discussing techniqueswe’ve chosen to sacrifice proofs of some, even basic,results—particularly where we can provide a good reference— in order to show how the methods are used to study moduli of curves. Likewise, we often prove results in special cases which we feel bring out the important ideas with a minimum of technical complication.