Introduction To Moduli Problems And Orbit Spaces

Author : P. E. Newstead
Publisher : Alpha Science International Limited
Page : 166 pages
File Size : 52,7 Mb
Release : 2012
Category : Mathematics
ISBN : 8184871627

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Introduction to Moduli Problems and Orbit Spaces by P. E. Newstead Pdf

Geometric Invariant Theory (GIT), developed in the 1960s by David Mumford, is the theory of quotients by group actions in Algebraic Geometry. Its principal application is to the construction of various moduli spaces. Peter Newstead gave a series of lectures in 1975 at the Tata Institute of Fundamental Research, Mumbai on GIT and its application to the moduli of vector bundles on curves. It was a masterful yet easy to follow exposition of important material, with clear proofs and many examples. The notes, published as a volume in the TIFR lecture notes series, became a classic, and generations of algebraic geometers working in these subjects got their basic introduction to this area through these lecture notes. Though continuously in demand, these lecture notes have been out of print for many years. The Tata Institute is happy to re-issue these notes in a new print.

Author : P. E. Newstead
Publisher : Unknown
Page : 368 pages
File Size : 42,5 Mb
Release : 1978
Category : Mathematics
ISBN : UCSC:32106005975039

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Lectures on Introduction to Moduli Problems and Orbit Spaces by P. E. Newstead Pdf

Author : Shigeru Mukai
Publisher : Cambridge University Press
Page : 528 pages
File Size : 46,5 Mb
Release : 2003-09-08
Category : Mathematics
ISBN : 0521809061

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An Introduction to Invariants and Moduli by Shigeru Mukai Pdf

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Author : Daniel Huybrechts,Manfred Lehn
Publisher : Cambridge University Press
Page : 345 pages
File Size : 46,8 Mb
Release : 2010-05-27
Category : Mathematics
ISBN : 9781139485821

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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 : Joe Harris,Ian Morrison
Publisher : Springer Science & Business Media
Page : 369 pages
File Size : 42,7 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227375

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Moduli of Curves by Joe Harris,Ian Morrison Pdf

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.

Author : Steve Bradlow
Publisher : Cambridge University Press
Page : 516 pages
File Size : 55,9 Mb
Release : 2009-05-21
Category : Mathematics
ISBN : 9780521734714

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Moduli Spaces and Vector Bundles by Steve Bradlow Pdf

Coverage includes foundational material as well as current research, authored by top specialists within their fields.

Author : Paul Hacking,Radu Laza,Dragos Oprea
Publisher : Birkhäuser
Page : 135 pages
File Size : 47,9 Mb
Release : 2016-02-04
Category : Mathematics
ISBN : 9783034809214

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Compactifying Moduli Spaces by Paul Hacking,Radu Laza,Dragos Oprea Pdf

This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps. Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.

Author : Jens Thomas Alexander Lang
Publisher : Herbert Utz Verlag
Page : 152 pages
File Size : 55,6 Mb
Release : 2001
Category : Electronic
ISBN : 3896758942

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Relative Moduli Spaces of Semi-stable Sheaves on Families of Curves by Jens Thomas Alexander Lang Pdf

Author : Igor Dolgachev
Publisher : Cambridge University Press
Page : 244 pages
File Size : 50,5 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0521525489

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Lectures on Invariant Theory by Igor Dolgachev Pdf

The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Author : A. Bialynicki-Birula,J. Carrell,W.M. McGovern
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 52,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662050712

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Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action by A. Bialynicki-Birula,J. Carrell,W.M. McGovern Pdf

This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.

Author : N.P. Landsman,Markus Pflaum,Martin Schlichenmaier
Publisher : Birkhäuser
Page : 360 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883641

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Quantization of Singular Symplectic Quotients by N.P. Landsman,Markus Pflaum,Martin Schlichenmaier Pdf

This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.

Author : Piotr Pragacz
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 49,6 Mb
Release : 2008-03-12
Category : Mathematics
ISBN : 3764385375

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Algebraic Cycles, Sheaves, Shtukas, and Moduli by Piotr Pragacz Pdf

Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.

Author : Eckart Viehweg
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642797453

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Quasi-projective Moduli for Polarized Manifolds by Eckart Viehweg Pdf

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.

Author : Leticia Brambila Paz,Ciro Ciliberto,Eduardo Esteves,Margarida Melo,Claire Voisin
Publisher : Springer
Page : 242 pages
File Size : 45,7 Mb
Release : 2017-10-03
Category : Mathematics
ISBN : 9783319594866

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Moduli of Curves by Leticia Brambila Paz,Ciro Ciliberto,Eduardo Esteves,Margarida Melo,Claire Voisin Pdf

Providing a timely description of the present state of the art of moduli spaces of curves and their geometry, this volume is written in a way which will make it extremely useful both for young people who want to approach this important field, and also for established researchers, who will find references, problems, original expositions, new viewpoints, etc. The book collects the lecture notes of a number of leading algebraic geometers and in particular specialists in the field of moduli spaces of curves and their geometry. This is an important subject in algebraic geometry and complex analysis which has seen spectacular developments in recent decades, with important applications to other parts of mathematics such as birational geometry and enumerative geometry, and to other sciences, including physics. The themes treated are classical but with a constant look to modern developments (see Cascini, Debarre, Farkas, and Sernesi's contributions), and include very new material, such as Bridgeland stability (see Macri's lecture notes) and tropical geometry (see Chan's lecture notes).

Author : Alberto Conte
Publisher : Springer
Page : 322 pages
File Size : 40,6 Mb
Release : 2006-11-17
Category : Mathematics
ISBN : 9783540393429

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Algebraic Threefolds by Alberto Conte Pdf