The moment-weight inequality and the Hilbert-Mumford criterion : GIT from the differential geometric viewpoint
著者
書誌事項
The moment-weight inequality and the Hilbert-Mumford criterion : GIT from the differential geometric viewpoint
（Lecture notes in mathematics, v. 2297）
Springer, c2021
- : pbk
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注記
Includes bibliographical references (p. 185-188) and index
内容説明・目次
内容説明
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.
目次
- 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.
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