Kirwan surjectivity for the equivariant Dolbeault cohomology

JOURNAL OF GEOMETRY AND PHYSICS

卷:144

Article

Lin, Yi¹ 

[1] Georgia Southern Univ, Dept Math Sci, Statesboro, GA 30460 USA

关键词: Kahler quotient;    Moment maps;    Cartan-Chern-Weil theory;   

DOI  :  10.1016/j.geomphys.2019.05.005

来源: Elsevier

【 摘 要 】

Consider the holomorphic Hamiltonian action of a compact Lie group K on a compact Kahler manifold M with a moment map Phi : M -> k*. Assume that 0 is a regular value of the moment map. Weitsman raised the question of what we can say about the cohomology of the Kahler quotient M-0 := Phi(-1)(0)/K if all the ordinary cohomology of M is of type (p, p). In this paper, using the Cartan-Chern-Weil theory we show that in the above context there is a natural surjective Kirwan map from an equivariant version of the Dolbeault cohomology of M onto the Dolbeault cohomology of the Kahler quotient M-0. As an immediate consequence, this result provides an answer to the question posed by Weitsman. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free