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Introduction to Geometric Invariant Theory by I.V. Dolgachev is a nonfiction available to read on EtoBox.

What is Introduction to Geometric Invariant Theory about?

These notes originate in a series of lectures given at the Tokyo Metropolitan University and Seoul National University in the Fall of 1993. These lectures have been extended into a graduate course at the University of Michigan in the Winter of 1994. Almost all of the material in these notes had been actually covered in my course. The main purpose of the notes is to provide a digest to Mumford’s book. Their sole novelty is the greater emphasis on dependence of the quotients on linearization of actions and also including toric varieties as examples of torus quotients of open subsets of affine space. We also briefly discuss Nagata’s counter-example to Hilbert’s Fourteenth Problem. Lack of time (and of interested audience) did not allow me to include such topic as the relationship between geometric invariant theory quotients and symplectic reductions. Only one application to moduli problem is included. This is Mumford’s construction of the moduli space of algebraic curves. The more knowledgeable reader will immediately recognize that the contents of these notes represent a small portion of material related to geometric invariant theory. Some compensation for this incompleteness can be

Who reads Introduction to Geometric Invariant Theory?

Author

I.V. Dolgachev

Publisher

Seoul National University

Published

1994

Language

EN

Category

nonfiction

Subjects

Mathematics, Geometry And Topology, Stem