Theory Of Moduli

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Geometry of Moduli Spaces and Representation Theory

Author : Roman Bezrukavnikov
Publisher : American Mathematical Soc.
ISBN 13 : 1470435748
Total Pages : 436 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometry of Moduli Spaces and Representation Theory by : Roman Bezrukavnikov

Download or read book Geometry of Moduli Spaces and Representation Theory written by Roman Bezrukavnikov and published by American Mathematical Soc.. This book was released on 2017-12-15 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

Moduli Spaces of Riemann Surfaces

Author : Benson Farb
Publisher : American Mathematical Soc.
ISBN 13 : 0821898876
Total Pages : 371 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Moduli Spaces of Riemann Surfaces by : Benson Farb

Download or read book Moduli Spaces of Riemann Surfaces written by Benson Farb and published by American Mathematical Soc.. This book was released on 2013-08-16 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Moduli Space of Curves

Author : Robert H. Dijkgraaf
Publisher : Springer Science & Business Media
ISBN 13 : 1461242649
Total Pages : 570 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Moduli Space of Curves by : Robert H. Dijkgraaf

Download or read book The Moduli Space of Curves written by Robert H. Dijkgraaf and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Moduli in Modern Mapping Theory

Author : Olli Martio
Publisher : Springer Science & Business Media
ISBN 13 : 0387855882
Total Pages : 368 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Moduli in Modern Mapping Theory by : Olli Martio

Download or read book Moduli in Modern Mapping Theory written by Olli Martio and published by Springer Science & Business Media. This book was released on 2008-11-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.

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.

Moduli Spaces

Author : Leticia Brambila
Publisher : Cambridge University Press
ISBN 13 : 1107636388
Total Pages : 347 pages
Book Rating : 4.1/5 (76 download)

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Book Synopsis Moduli Spaces by : Leticia Brambila

Download or read book Moduli Spaces written by Leticia Brambila and published by Cambridge University Press. This book was released on 2014-03-13 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

Moduli of Curves

Author : Joe Harris
Publisher : Springer Science & Business Media
ISBN 13 : 0387227377
Total Pages : 381 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Moduli of Curves by : Joe Harris

Download or read book Moduli of Curves written by Joe Harris and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results and open problems about important topics which are not covered in detail.

Approximation Theory

Author : George A. Anastassiou
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641511
Total Pages : 554 pages
Book Rating : 4.6/5 (415 download)

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Book Synopsis Approximation Theory by : George A. Anastassiou

Download or read book Approximation Theory written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 1999-12-22 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop erty (GSPP) for almost all known linear approximation operators of ap proximation theory including: trigonometric operators and algebraic in terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.

Advances in Moduli Theory

Author : Kenji Ueno
Publisher : American Mathematical Soc.
ISBN 13 : 9780821821565
Total Pages : 328 pages
Book Rating : 4.8/5 (215 download)

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Book Synopsis Advances in Moduli Theory by : Kenji Ueno

Download or read book Advances in Moduli Theory written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 2002 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The word ``moduli'' in the sense of this book first appeared in the epoch-making paper of B. Riemann, Theorie der Abel'schen Funktionen, published in 1857. Riemann defined a Riemann surface of an algebraic function field as a branched covering of a one-dimensional complex projective space, and found out that Riemann surfaces have parameters. This work gave birth to the theory of moduli. However, the viewpoint regarding a Riemann surface as an algebraic curve became the mainstream,and the moduli meant the parameters for the figures (graphs) defined by equations. In 1913, H. Weyl defined a Riemann surface as a complex manifold of dimension one. Moreover, Teichmuller's theory of quasiconformal mappings and Teichmuller spaces made a start for new development of the theory ofmoduli, making possible a complex analytic approach toward the theory of moduli of Riemann surfaces. This theory was then investigated and made complete by Ahlfors, Bers, Rauch, and others. However, the theory of Teichmuller spaces utilized the special nature of complex dimension one, and it was difficult to generalize it to an arbitrary dimension in a direct way. It was Kodaira-Spencer's deformation theory of complex manifolds that allowed one to study arbitrary dimensional complex manifolds.Initial motivation in Kodaira-Spencer's discussion was the need to clarify what one should mean by number of moduli. Their results, together with further work by Kuranishi, provided this notion with intrinsic meaning. This book begins by presenting the Kodaira-Spencer theory in its original naiveform in Chapter 1 and introduces readers to moduli theory from the viewpoint of complex analytic geometry. Chapter 2 briefly outlines the theory of period mapping and Jacobian variety for compact Riemann surfaces, with the Torelli theorem as a goal. The theory of period mappings for compact Riemann surfaces can be generalized to the theory of period mappings in terms of Hodge structures for compact Kahler manifolds. In Chapter 3, the authors state the theory of Hodge structures, focusingbriefly on period mappings. Chapter 4 explains conformal field theory as an application of moduli theory. This is the English translation of a book originally published in Japanese. Other books by Kenji Ueno published in this AMS series, Translations of Mathematical Monographs, include An Introduction toAlgebraic Geometry, Volume 166, Algebraic Geometry 1: From Algebraic Varieties to Schemes, Volume 185, and Algebraic Geometry 2: Sheaves and Cohomology, Volume 197.

Quasi-projective Moduli for Polarized Manifolds

Author : Eckart Viehweg
Publisher : Springer Science & Business Media
ISBN 13 : 3642797458
Total Pages : 329 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Quasi-projective Moduli for Polarized Manifolds by : Eckart Viehweg

Download or read book Quasi-projective Moduli for Polarized Manifolds written by Eckart Viehweg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of moduli goes back to B. Riemann, who shows in [68] that the isomorphism class of a Riemann surface of genus 9 ~ 2 depends on 3g - 3 parameters, which he proposes to name "moduli". A precise formulation of global moduli problems in algebraic geometry, the definition of moduli schemes or of algebraic moduli spaces for curves and for certain higher dimensional manifolds have only been given recently (A. Grothendieck, D. Mumford, see [59]), as well as solutions in some cases. It is the aim of this monograph to present methods which allow over a field of characteristic zero to construct certain moduli schemes together with an ample sheaf. Our main source of inspiration is D. Mumford's "Geometric In variant Theory". We will recall the necessary tools from his book [59] and prove the "Hilbert-Mumford Criterion" and some modified version for the stability of points under group actions. As in [78], a careful study of positivity proper ties of direct image sheaves allows to use this criterion to construct moduli as quasi-projective schemes for canonically polarized manifolds and for polarized manifolds with a semi-ample canonical sheaf.

Deformations of Algebraic Schemes

Author : Edoardo Sernesi
Publisher : Springer Science & Business Media
ISBN 13 : 3540306153
Total Pages : 343 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Deformations of Algebraic Schemes by : Edoardo Sernesi

Download or read book Deformations of Algebraic Schemes written by Edoardo Sernesi and published by Springer Science & Business Media. This book was released on 2007-04-20 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This account of deformation theory in classical algebraic geometry over an algebraically closed field presents for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet relevant to algebraic geometers. Many examples are provided. Most of the algebraic results needed are proved. The style of exposition is kept at a level amenable to graduate students with an average background in algebraic geometry.

Moduli Spaces and Vector Bundles

Author : Steve Bradlow
Publisher : Cambridge University Press
ISBN 13 : 0521734711
Total Pages : 516 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Moduli Spaces and Vector Bundles by : Steve Bradlow

Download or read book Moduli Spaces and Vector Bundles written by Steve Bradlow and published by Cambridge University Press. This book was released on 2009-05-21 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coverage includes foundational material as well as current research, authored by top specialists within their fields.

Deformation Theory

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
ISBN 13 : 1441915966
Total Pages : 241 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Deformation Theory by : Robin Hartshorne

Download or read book Deformation Theory written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2009-11-12 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.

Geometry of Moduli

Author : Jan Arthur Christophersen
Publisher : Springer
ISBN 13 : 9783319948805
Total Pages : 0 pages
Book Rating : 4.9/5 (488 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 0 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.

Dynamical Aspects of Teichmüller Theory

Author : Carlos Matheus Silva Santos
Publisher : Springer
ISBN 13 : 3319921592
Total Pages : 122 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Dynamical Aspects of Teichmüller Theory by : Carlos Matheus Silva Santos

Download or read book Dynamical Aspects of Teichmüller Theory written by Carlos Matheus Silva Santos and published by Springer. This book was released on 2018-07-09 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a remarkable contribution to the literature on dynamical systems and geometry. It consists of a selection of work in current research on Teichmüller dynamics, a field that has continued to develop rapidly in the past decades. After a comprehensive introduction, the author investigates the dynamics of the Teichmüller flow, presenting several self-contained chapters, each addressing a different aspect on the subject. The author includes innovative expositions, all the while solving open problems, constructing examples, and supplementing with illustrations. This book is a rare find in the field with its guidance and support for readers through the complex content of moduli spaces and Teichmüller Theory. The author is an internationally recognized expert in dynamical systems with a talent to explain topics that is rarely found in the field. He has created a text that would benefit specialists in, not only dynamical systems and geometry, but also Lie theory and number theory.

Geometric Invariant Theory

Author : David Mumford
Publisher : Springer
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Geometric Invariant Theory by : David Mumford

Download or read book Geometric Invariant Theory written by David Mumford and published by Springer. This book was released on 1982 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.