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On indices of meromorphic 1-forms

Published online by Cambridge University Press:  04 December 2007

W. Ebeling  and
S. M. Gusein-Zade
W. Ebeling
Affiliation:
Universität Hannover, Institut für Mathematik, Postfach 6009, D-30060 Hannover, Germanyebeling@math.uni-hannover.de
S. M. Gusein-Zade
Affiliation:
Moscow State University, Faculty of Mechanics and Mathematics, Moscow, 119992, Russiasabir@mccme.ru
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Abstract

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We discuss meromorphic 1-forms on compact complex manifolds and on complete intersections with isolated singularities. We give a Poincaré–Hopf type formula for them, i.e. we express the Euler characteristic in terms of singularities of a meromorphic 1-form. For that we introduce a suitable notion of an index of a germ of a meromorphic 1-form (with an additional structure) on an isolated complete intersection singularity. For a meromorphic 1-form on a complete intersection V with isolated singularities the indices of the singular points sum up to (plus–minus) the Euler characteristic of a smoothing of V.

Keywords

meromorphic 1-formssingular pointsindices32Q5514B0532A20
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 3 , May 2004 , pp. 809 - 817
Copyright
Foundation Compositio Mathematica 2004