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Introduction to Moduli Problems and Orbit Spaces
P. E. Newstead, University of Liverpool, England
A publication of the Tata Institute of Fundamental Research.
Tata Institute of Fundamental Research
2011; 152 pp; softcover
ISBN-10: 81-8487-162-7
ISBN-13: 978-81-8487-162-3
List Price: US$40
Member Price: US$32
Order Code: TIFR/17
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Geometric Invariant Theory (GIT), developed in the 1960s by David Mumford, is the theory of quotients by group actions in algebraic geometry. The theory's principal application is to the construction of various moduli spaces.

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 and understandable 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 reissue these notes in this volume.

A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka.


Graduate students and research mathematicians interested in algebraic geometry.

Table of Contents

  • Preliminaries
  • The concept of moduli
  • Endomorphisms of vector spaces
  • Quotients
  • Examples
  • Vector bundles over a curve
  • Bibliography
  • List of symbols
  • Index
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