G-invariant Holomorphic Morse inequalities

2015/06/15 by Martin Puchol, Puchol, Martin
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1506.04526

arxiv created 2015/11/17 · arxiv updated 2015/11/19

Abstract

Consider an action of a connected compact Lie group on a compact complex manifold M, and two equivariant vector bundles L and E on M, with L of rank 1. The purpose of this paper is to establish holomorphic Morse inequalities à la Demailly for the invariant part of the Dolbeault cohomology of tensor powers of L twisted by E. To do so, we define a moment map μ by the Kostant formula and we define the reduction of M under a natural hypothesis on μ^-1(0). Our inequalities are given in term of the curvature of the bundle induced by L on this reduction.

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