Abstract
Abstract We obtain estimates on the character of the cohomology of an S1-equivariant holomorphic vector bundle over a Kähler manifold M in terms of the cohomology of the Lerman symplectic cuts and the symplectic reduction of M. In particular, we prove and extend inequalities conjectured by Wu and Zhang. The proof is based on constructing a flat family of complex spaces Mt (t ∈ ℂ) such that Mt is isomorphic to M for t ≠ 0, while M0 is a singular reducible complex space, whose irreducible components are the Lerman symplectic cuts.
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