The moment-weight inequality and the Hilbert-Mumford criterion : GIT from the differential geometric viewpoint / Valentina Georgoulas, Joel W. Robbin, and Dietmar Arno Salamon.

Format:

Book

Author/Creator:

Georgoulas, Valentina, author.

Salamon, D. (Dietmar), author.

Robbin, Joel W., author.

Series:

Lecture Notes in Mathematics

Lecture Notes in Mathematics ; v.2297

Language:

English

Subjects (All):

Invariants.

Geometry, Differential.

Geometry, Algebraic.

Physical Description:

1 online resource (193 pages)

Place of Publication:

Cham, Switzerland : Springer, [2021]

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.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Georgoulas, Valentina The Moment-Weight Inequality and the Hilbert-Mumford Criterion

ISBN:

3-030-89300-6

OCLC:

1290839423