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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2017: 1.49

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Volume 1999, Issue 508


Symplectic cutting of Kähler manifolds

Maxim Braverman
Published Online: 2008-06-11 | DOI: https://doi.org/10.1515/crll.1999.508.85


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.

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 M 0 is a singular reducible complex space, whose irreducible components are the Lerman symplectic cuts.

About the article

Received: 1998-02-12

Accepted: 1998-08-11

Published Online: 2008-06-11

Published in Print: 1999-03-12

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 1999, Issue 508, Pages 85–98, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crll.1999.508.85.

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