The moment-weight inequality and the Hilbert-Mumford criterion : GIT from the differential geometric viewpoint
Author(s)
Bibliographic Information
The moment-weight inequality and the Hilbert-Mumford criterion : GIT from the differential geometric viewpoint
（Lecture notes in mathematics, v. 2297）
Springer, c2021
- : pbk
Available at / 27 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkL/N||LNM||2297200043175995
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliographical references (p. 185-188) and index
Description and Table of Contents
Description
This book provides an introduction to geometric invariant theory from a differential geometric viewpoint. It is inspired by certain infinite-dimensional analogues of geometric invariant theory that arise naturally in several different areas of geometry. The central ingredients are the moment-weight inequality relating the Mumford numerical invariants to the norm of the moment map, the negative gradient flow of the moment map squared, and the Kempf--Ness function. The exposition is essentially self-contained, except for an appeal to the Lojasiewicz gradient inequality. A broad variety of examples illustrate the theory, and five appendices cover essential topics that go beyond the basic concepts of differential geometry. The comprehensive bibliography will be a valuable resource for researchers.
The book is addressed to graduate students and researchers interested in geometric invariant theory and related subjects. It will be easily accessible to readers with a basic understanding of differential geometry and does not require any knowledge of algebraic geometry.
Table of Contents
- Introduction. - The Moment Map. - The Moment Map Squared. - The Kempf-Ness Function. - -Weights. - The Moment-Weight Inequality. - Stability in Symplectic Geometry. - Stability in Algebraic Geometry. - Rationality. - The Dominant -Weight. - Torus Actions. - The Hilbert-Mumford Criterion. - Critical Orbits.
by "Nielsen BookData"