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Compositio Mathematica (2004), 140 : 809-817 Cambridge University Press
Copyright © Foundation Compositio Mathematica 2004
doi:10.1112/S0010437X03000691
 

On indices of meromorphic 1-forms

W. Ebeling a1 and S. M. Gusein-Zade a2
a1 Universität Hannover, Institut für Mathematik, Postfach 6009, D-30060 Hannover, Germany ebeling@math.uni-hannover.de
a2 Moscow State University, Faculty of Mechanics and Mathematics, Moscow, 119992, Russia sabir@mccme.ru

Article author query
ebeling w   [Google Scholar] 
gusein-zade s   [Google Scholar] 
 

Abstract

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.

(Received March 14 2002)
(Accepted July 24 2002)


Key Words: meromorphic 1-forms; singular points; indices.

Maths Classification

32Q55; 14B05; 32A20.

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