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The Moment-Weight Inequality and the Hilbert-Mumford Criterion : GIT from the Differential Geometric Viewpoint / by Valentina Georgoulas, Joel W. Robbin, Dietmar Arno Salamon.
- Format:
- Book
- Author/Creator:
- Georgoulas, Valentina, Author.
- Robbin, Joel W., Author.
- Salamon, Dietmar Arno., Author.
- Series:
- Mathematics and Statistics (SpringerNature-11649)
- Lecture Notes in Mathematics, 1617-9692 ; 2297
- Language:
- English
- Subjects (All):
- Geometry, Differential.
- Geometry, Algebraic.
- Differential Geometry.
- Algebraic Geometry.
- Local Subjects:
- Differential Geometry.
- Algebraic Geometry.
- Physical Description:
- 1 online resource (VII, 192 pages) : 3 illustrations in color.
- Edition:
- 1st ed. 2021.
- Contained In:
- Springer Nature eBook
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2021.
- System Details:
- text file PDF
- Summary:
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 978-3-030-89300-2
- 9783030893002
- Access Restriction:
- Restricted for use by site license.
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