The Moment-Weight Inequality and the Hilbert–Mumford Criterion: GIT from the Differential Geometric Viewpoint (1st ed. 2021) (Lecture Notes in Mathematics #2297)
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- Synopsis
- 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.
- Copyright:
- 2021
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9783030893002
- Related ISBNs:
- 9783030892999
- Publisher:
- Springer International Publishing
- Date of Addition:
- 01/01/22
- Copyrighted By:
- The Editor
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Categories:
- Nonfiction, Mathematics and Statistics
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.
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