The moment-weight inequality and the Hilbert-Mumford criterion : GIT from the differential geometric viewpoint / Valentina Georgoulas, Joel W. Robbin, Dietmar Arno Salamon.
The moment-weight inequality and the Hilbert-Mumford criterion : GIT from the differential geometric viewpoint / Valentina Georgoulas, Joel W. Robbin, Dietmar Arno Salamon.
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.
Bibliography, etc. Note
Includes bibliographical references (pages 185-188) and index.
