Symplectic cutting of Kaehler manifolds

Details Symplectic cutting of Kaehler manifolds Symplectic cutting of Kaehler manifolds

1997-12-19

arxiv.org/abs/alg-geom/9712024v1

Mathematics

Algebraic Geometry

11 pages, LaTeX 2e

Scientific paper

We obtain estimates on the character of the cohomology of an $S^1$-equivariant holomorphic vector bundle over a Kaehler 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 $M_t$ such that $M_t$ is isomorphic to $M$ for $t\not=0$, while $M_0$ is a singular reducible complex space, whose irreducible components are the Lerman symplectic cuts.

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