Symmetries in generalized Kähler geometry

Yi Lin; Susan Tolman

doi:10.1007/s00220-006-0096-z

Symmetries in generalized Kähler geometry

Yi Lin
, Susan Tolman

Mathematical Sciences

University of Illinois at Urbana-Champaign

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

We define the notion of a moment map and reduction in both generalized complex geometry and generalized Kähler geometry. As an application, we give very simple explicit constructions of bi-Hermitian structures on ℂdouble struck P sign^N, Hirzebruch surfaces, the blow up of ℂdouble struck P sign^N at arbitrarily many points, and other toric varieties, as well as complex Grassmannians.

Original language	English
Pages (from-to)	199-222
Number of pages	24
Journal	Communications in Mathematical Physics
Volume	268
Issue number	1
DOIs	https://doi.org/10.1007/s00220-006-0096-z
State	Published - Nov 2006

Scopus Subject Areas

Statistical and Nonlinear Physics
Mathematical Physics

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AB - We define the notion of a moment map and reduction in both generalized complex geometry and generalized Kähler geometry. As an application, we give very simple explicit constructions of bi-Hermitian structures on ℂdouble struck P signN, Hirzebruch surfaces, the blow up of ℂdouble struck P signN at arbitrarily many points, and other toric varieties, as well as complex Grassmannians.

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JO - Communications in Mathematical Physics

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Symmetries in generalized Kähler geometry

Abstract

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