Symmetries in generalized Kähler geometry
type: Item
instance of: scholarly article
title: Symmetries in generalized Kähler geometry
zbMATH Open document ID: 1120.53049
author: Yi Lin
author: Susan Tolman
published in: Communications in Mathematical Physics
publication date: 2007-05-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0509069
review text: Generalized complex geometry, as developed by Hitchin, interpolates between complex and symplectic manifolds. On the other hand, Marco Gualtieri showed that generalized Kähler geometry is equivalent to a bi-Hermitian geometry with torsion, first discovered by physicists. The article under review defines momentum map and reduction in both, generalized complex geometry and generalized Kähler geometry. They obtain, as applications, explicit constructions of bi-Hermitian structures on manifolds which can be obtained as the symplectic quotient of \(\mathbb{C}^N\), i.e., \(\mathbb{C}\mathbb{P}^N\), Hirzebruch surfaces, the blow up of \(\mathbb{C}\mathbb{P}^N\) at arbitrarily many points, and other toric varieties, as well as complex Grassmannians. Their constructions carry over to the twisted case. The paper under review also compares their results with others in this field.
Mathematics Subject Classification ID: 53D20
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 5159642
zbMATH Keywords: symmetries
zbMATH Keywords: Kähler geometry
zbMATH Keywords: generalized Kähler geometry
zbMATH Keywords: moment map
zbMATH Keywords: symplectic reduction
zbMATH Keywords: generalized complex geometry
reviewed by: L. Del Riego
MaRDI profile type: Publication
OpenAlex ID: W1986022669
arXiv ID: math/0509069
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DOI: 10.1007/S00220-006-0096-Z
description: scientific article