Momentum maps and reduction in algebraic geometry
type: Item
instance of: scholarly article
title: Momentum maps and reduction in algebraic geometry
zbMATH Open document ID: 0955.37031
DOI: 10.1016/S0926-2245(98)00020-5
published in: Differential Geometry and its Applications
publication date: 2000-09-28T00:00:00Z
review text: The paper gives a brief survey of the works in the last fifteen years devoted to the study of the geometry of the momentum map with applications to symplectic geometry and to related topics in algebraic geometry. The problem of understanding how the geometry and topology of the symplectic reduction at a coadjoint orbit varies as the orbit varies and what happens when the symplectic reduction acquires singularities is discussed. This problem is explained to be related to the corresponding questions in algebraic geometry, namely, how the quotient varieties which arise in Mumford's geometric invariant theory vary with the linearization of the group action and how their singularities appear. The relations of the problems mentioned above with the theory of moduli spaces of vector bundles, residue formulae and nonabelian localization problems and with the theory of Yang-Mills equations are also indicated.
reviewed by: S. V. Zelik
Mathematics Subject Classification ID: 37J15
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 37-02
zbMATH DE Number: 1308132
zbMATH Keywords: symplectic geometry
zbMATH Keywords: reduction
zbMATH Keywords: momentum map
zbMATH Keywords: moduli space
Wikidata QID: Q115337483
author: Frances Kirwan
MaRDI profile type: Publication
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