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Jump formulas in Hamiltonian Geometry

Paul-Emile Paradan
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Abstract

This paper is concerned with the Hamiltonian actions of a torus on a symplectic manifold. We are interested here in two global invariants: the Duistermaat-Heckman measure DH(M), and the Riemann-Roch chatacters RR(M,L^k),k>0, which are defined when the symplectic manifold is prequantized by a Kostant-Souriau line bundle L. We can associate to each connected component C of regular values of the moment map the following local invariants: the polynomial DH_c which coincides with DH(M) on C, and the periodic polynomial m_c which computes the multiplicity of RR(M,L^k), k>0, in the cone generated by C. The purpose of this paper is to compute the differences DH_c - DH_c' and m_c - m_c' when C and C' are two adjacent connected components of regular values of the moment map.

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Paul-Emile Paradan. 2004-11-13. Jump formulas in Hamiltonian Geometry. https://arxiv.org/abs/math/0411306

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