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Symplectic cutting of Kähler manifolds
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Maxim Braverman
Published/Copyright:
June 11, 2008
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.
Received: 1998-02-12
Accepted: 1998-08-11
Published Online: 2008-06-11
Published in Print: 1999-03-12
© Walter de Gruyter
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Articles in the same Issue
- On nonpositively curved euclidean submanifolds: splitting results II
- Extremal lengths of homology classes on Riemann surfaces
- Addendum and erratum to An absolute Siegel's Lemma
- Is a linear space contained in a submanifold? – On the number of derivatives needed to tell
- Caractères à valeurs dans le centre de Bernstein
- Symplectic cutting of Kähler manifolds
- Automorphism groups of 3-dimensional complex tori
- Invariants of algebraic groups
- Weights of Markov traces on Hecke algebras
- On the proportion of quadratic character twists of L-functions attached to cusp forms not vanishing at the central point
- The Pfaffian closure of an o-minimal structure
- Subvarieties of ℂn with non-extendable automorphisms
