The Moment-Weight Inequality and the Hilbert-Mumford Criterion
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Date
2021Type
- Monograph
ETH Bibliography
yes
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Abstract
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. Show more
Publication status
publishedJournal / series
Lecture Notes in MathematicsVolume
Publisher
SpringerSubject
Symplectic Geometry; Kähler Manifold; Hamiltonian Group Action; Moment Map; Mumford Weights; Kempf-Ness Function; Moment-weight Inequality; Hilbert-Mumford Criterion; Geometric Invariant TheoryRelated publications and datasets
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ETH Bibliography
yes
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