Author: P. E. Newstead
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 366

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Book Description

Author: P. E. Newstead
Publisher: Alpha Science International Limited
ISBN: 9788184871623
Category : Mathematics
Languages : en
Pages : 166

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Book Description
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: Maurizio Cornalba
Publisher: World Scientific
ISBN: 9814590878
Category : Mathematics
Languages : en
Pages : 716

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Author: Igor Dolgachev
Publisher: Cambridge University Press
ISBN: 9780521525480
Category : Mathematics
Languages : en
Pages : 244

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Book Description
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: Piotr Pragacz
Publisher: Springer Science & Business Media
ISBN: 3764385375
Category : Mathematics
Languages : en
Pages : 240

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Book Description
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: Shigeru Mukai
Publisher: Cambridge University Press
ISBN: 9780521809061
Category : Mathematics
Languages : en
Pages : 528

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Author: Leticia Brambila-Paz
Publisher: Cambridge University Press
ISBN: 1139480049
Category : Mathematics
Languages : en
Pages : 506

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Book Description
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.

Author: Alberto Conte
Publisher: Springer
ISBN: 3540393420
Category : Mathematics
Languages : en
Pages : 322

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Book Description

Author: Daniel Huybrechts
Publisher: Cambridge University Press
ISBN: 1139485822
Category : Mathematics
Languages : en
Pages : 345

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Book Description
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: Paul Hacking
Publisher: Birkhäuser
ISBN: 3034809212
Category : Mathematics
Languages : en
Pages : 141

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Book Description
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.