The Moment-Weight Inequality and the Hilbert-Mumford Criterion

Anglický jazyk

The Moment-Weight Inequality and the Hilbert-Mumford Criterion

Vydavateľstvo: Springer International Publishing
Rok vydania: 2021
Formát: Paperback
Rozmer: 235 x 155 mm
Jazyk: Anglický jazyk
ISBN: 9783030892999

Na objednávku, dodanie 2-4 týždne

54.44 €

bežná cena: 60.49 €

O knihe

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.