Symplectic cutting of Kähler manifolds. (English) Zbl 0915.32009
We obtain estimates on the character of the cohomology of an \(S^1\)-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.
Reviewer: M.Braverman (Jerusalem)
MSC:
32L05 | Holomorphic bundles and generalizations |
32C35 | Analytic sheaves and cohomology groups |
53D20 | Momentum maps; symplectic reduction |
58J20 | Index theory and related fixed-point theorems on manifolds |