Algebraic Structures And Moduli Spaces

Author : Jacques Hurtubise
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 41,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821835685

Get Book

Algebraic Structures and Moduli Spaces by Jacques Hurtubise Pdf

This book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties. Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kota Yoshioka, explains their recent work on the moduli space of instantons over ${\mathbb R 4$. The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.

Author : Jacques Hurtubise and Eyal Markman
Publisher : American Mathematical Soc.
Page : 268 pages
File Size : 48,7 Mb
Release : 2024-07-01
Category : Algebra, Abstract
ISBN : 0821870335

Get Book

Algebraic Structures and Moduli Spaces by Jacques Hurtubise and Eyal Markman Pdf

This book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties. Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kota Yoshioka, explains their recent work on the moduli space of instantons over ${\mathbb R 4$. The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.

Author : O. A. Laudal
Publisher : Springer
Page : 165 pages
File Size : 42,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385325

Get Book

Formal Moduli of Algebraic Structures by O. A. Laudal Pdf

Author : Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun
Publisher : American Mathematical Soc.
Page : 436 pages
File Size : 55,8 Mb
Release : 2017-12-15
Category : Algebraic varieties
ISBN : 9781470435745

Get Book

Geometry of Moduli Spaces and Representation Theory by Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun Pdf

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.

Author : Robert H. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242642

Get Book

The Moduli Space of Curves by Robert H. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer Pdf

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.

Author : Klaus Hulek,Constantin Kahn,Steven H. Weintraub
Publisher : Walter de Gruyter
Page : 361 pages
File Size : 49,7 Mb
Release : 2011-05-03
Category : Mathematics
ISBN : 9783110891928

Get Book

Moduli Spaces of Abelian Surfaces by Klaus Hulek,Constantin Kahn,Steven H. Weintraub Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Author : Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov
Publisher : Springer
Page : 231 pages
File Size : 40,7 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9783030029432

Get Book

Algebraic Curves by Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov Pdf

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

Author : Benson Farb,Richard Hain,Eduard Looijenga
Publisher : American Mathematical Soc.
Page : 371 pages
File Size : 40,5 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9780821898871

Get Book

Moduli Spaces of Riemann Surfaces by Benson Farb,Richard Hain,Eduard Looijenga Pdf

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.

Author : Hossein Abbaspour,Matilde Marcolli,Thomas Tradler
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 49,8 Mb
Release : 2010-04-21
Category : Mathematics
ISBN : 9783834896803

Get Book

Deformation Spaces by Hossein Abbaspour,Matilde Marcolli,Thomas Tradler Pdf

The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.

Author : Daniel Huybrechts,Manfred Lehn
Publisher : Cambridge University Press
Page : 345 pages
File Size : 42,6 Mb
Release : 2010-05-27
Category : Mathematics
ISBN : 9781139485821

Get Book

The Geometry of Moduli Spaces of Sheaves by Daniel Huybrechts,Manfred Lehn Pdf

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.

Author : Martin Olsson
Publisher : American Mathematical Society
Page : 313 pages
File Size : 43,6 Mb
Release : 2023-09-15
Category : Mathematics
ISBN : 9781470474805

Get Book

Algebraic Spaces and Stacks by Martin Olsson Pdf

This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix. It is splendid to have a self-contained treatment of stacks, written by a leading practitioner. Finally we have a reference where one can find careful statements and proofs of many of the foundational facts in this important subject. Researchers and students at all levels will be grateful to Olsson for writing this book. —William Fulton, University of Michigan This is a carefully planned out book starting with foundations and ending with detailed proofs of key results in the theory of algebraic stacks. —Johan de Jong, Columbia University

Author : Martin Olsson
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 48,5 Mb
Release : 2016-05-13
Category : Algebraic spaces
ISBN : 9781470427986

Get Book

Algebraic Spaces and Stacks by Martin Olsson Pdf

This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.

Author : Iku Nakamura,Lin Weng
Publisher : Amer Mathematical Society
Page : 479 pages
File Size : 46,6 Mb
Release : 2010-06
Category : Mathematics
ISBN : 4931469590

Get Book

Algebraic and Arithmetic Structures of Moduli Spaces(Sapporo 2007) by Iku Nakamura,Lin Weng Pdf

The conference "Algebraic and Arithmetic Structures of Moduli Spaces" was held in September 2007, at Sapporo (Hokkaido University). Twenty talks were delivered by invited speakers on arithmetic geometry, algebraic geometry and complex geometry. This volume is the proceedings of the conference, to be exact, a collection of eleven papers contributed by some of the speakers which have undergone rigorous refereeing. The topics that are discussed in the articles are diverse in nature such as class field theory, zeta functions, moduli of arithmetic vector bundles, moduli of complex vector bundles, moduli of abelian varieties and theory of display, moduli of Fermat varieties and some topics on cubic threefolds. Among others, the papers of Pappas-Rapoport, Rajan and Weng address many new interesting questions in the related fields, which seem to be worthy of reading for young researchers.

Author : Martin Doubek,Branislav Jurčo,Martin Markl,Ivo Sachs
Publisher : Springer Nature
Page : 223 pages
File Size : 42,6 Mb
Release : 2020-11-22
Category : Science
ISBN : 9783030530563

Get Book

Algebraic Structure of String Field Theory by Martin Doubek,Branislav Jurčo,Martin Markl,Ivo Sachs Pdf

This book gives a modern presentation of modular operands and their role in string field theory. The authors aim to outline the arguments from the perspective of homotopy algebras and their operadic origin. Part I reviews string field theory from the point of view of homotopy algebras, including A-infinity algebras, loop homotopy (quantum L-infinity) and IBL-infinity algebras governing its structure. Within this framework, the covariant construction of a string field theory naturally emerges as composition of two morphisms of particular odd modular operads. This part is intended primarily for researchers and graduate students who are interested in applications of higher algebraic structures to strings and quantum field theory. Part II contains a comprehensive treatment of the mathematical background on operads and homotopy algebras in a broader context, which should appeal also to mathematicians who are not familiar with string theory.

Author : Alexander Polishchuk
Publisher : Unknown
Page : 0 pages
File Size : 49,9 Mb
Release : 2022
Category : Electronic
ISBN : 398547026X

Get Book

A∞-structures and Moduli Spaces by Alexander Polishchuk Pdf