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

36 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 CP N , Hirzebruch surfaces, the blow up of CP N at arbitrarily many points, and other toric varieties, as well as complex Grassmannians.

Original language	American English
Journal	Communications in Mathematical Physics
Volume	268
DOIs	https://doi.org/10.1007/s00220-006-0096-z
State	Published - Nov 2006

Keywords

Generalized Kähler Geometry
Symmetries

DC Disciplines

Mathematics

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Cite this

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title = "Symmetries in Generalized K{\"a}hler Geometry",

abstract = " We define the notion of a moment map and reduction in both generalized complex geometry and generalized K{\"a}hler geometry. As an application, we give very simple explicit constructions of bi-Hermitian structures on CP N , Hirzebruch surfaces, the blow up of CP N at arbitrarily many points, and other toric varieties, as well as complex Grassmannians.",

keywords = "Generalized K{\"a}hler Geometry, Symmetries",

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doi = "10.1007/s00220-006-0096-z",

language = "American English",

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journal = "Communications in Mathematical Physics",

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AU - Tolman, Susan

N1 - 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 s

PY - 2006/11

Y1 - 2006/11

N2 - 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 CP N , Hirzebruch surfaces, the blow up of CP N at arbitrarily many points, and other toric varieties, as well as complex Grassmannians.

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 CP N , Hirzebruch surfaces, the blow up of CP N at arbitrarily many points, and other toric varieties, as well as complex Grassmannians.

KW - Generalized Kähler Geometry

KW - Symmetries

UR - https://doi.org/10.1007/s00220-006-0096-z

U2 - 10.1007/s00220-006-0096-z

DO - 10.1007/s00220-006-0096-z

M3 - Article

SN - 0010-3616

VL - 268

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

ER -

Symmetries in Generalized Kähler Geometry

Abstract

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