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

Bibliographic Information

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

Valentina Georgoulas, Joel W. Robbin, Dietmar Arno Salamon

(Lecture notes in mathematics, v. 2297)

Springer, c2021

  • : pbk

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Note

Includes bibliographical references (p. 185-188) and index

Description and Table of Contents

Description

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.

Table of Contents

- 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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Details

  • NCID
    BC11332805
  • ISBN
    • 9783030892999
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    vii, 190 p.
  • Size
    24 cm
  • Parent Bibliography ID
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