The Moment-Weight Inequality and the Hilbert–Mumford Criterion
The Moment-Weight Inequality and the Hilbert–Mumford Criterion:
GIT from the Differential Geometric Viewpoint
English | 2022 | ISBN: 3030892999 | 199 Pages | PDF EPUB | 14 MB
GIT from the Differential Geometric Viewpoint
English | 2022 | ISBN: 3030892999 | 199 Pages | PDF EPUB | 14 MB
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.