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The moment-weight inequality and the...

Georgoulas, Valentina.

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The moment-weight inequality and the Hilbert-Mumford criterion = GIT from the differential geometric viewpoint /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The moment-weight inequality and the Hilbert-Mumford criterion/ by Valentina Georgoulas, Joel W. Robbin, Dietmar Arno Salamon.
Reminder of title:	GIT from the differential geometric viewpoint /
Author:	Georgoulas, Valentina.
other author:	Robbin, Joel W.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	vii, 192 p. :ill. (chiefly col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometry, Differential. -
Online resource:	https://doi.org/10.1007/978-3-030-89300-2
ISBN:	9783030893002

The moment-weight inequality and the Hilbert-Mumford criterion = GIT from the differential geometric viewpoint /
Georgoulas, Valentina.

The moment-weight inequality and the Hilbert-Mumford criterionGIT from the differential geometric viewpoint /[electronic resource] :by Valentina Georgoulas, Joel W. Robbin, Dietmar Arno Salamon. - Cham :Springer International Publishing :2021. - vii, 192 p. :ill. (chiefly col.), digital ;24 cm. - Lecture notes in mathematics,v. 22971617-9692 ;. - Lecture notes in mathematics ;v. 2297..

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.

ISBN: 9783030893002

Standard No.: 10.1007/978-3-030-89300-2doiSubjects--Topical Terms:

523835
Geometry, Differential.

LC Class. No.: QA641 / .G46 2021

Dewey Class. No.: 516.36

The moment-weight inequality and the Hilbert-Mumford criterion = GIT from the differential geometric viewpoint /
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520 $a 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.
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