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Computing the cup product structure for complements of complex affine varieties

โœ Scribed by Uli Walther

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
240 KB
Volume
164
Category
Article
ISSN
0022-4049

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โœฆ Synopsis

Let X = C n . In this paper we present an algorithm that computes the cup product structure for the de Rham cohomology ring H โ€ข dR (U ; C) where U is the complement of an arbitrary Zariski-closed set Y in X . Our method relies on the fact that Tor is a balanced functor, a property which we make algorithmic, as well as a technique to extract explicit representatives of cohomology classes in a restriction or integration complex. We also present an alternative approach to computing V -strict resolutions of complexes that is seemingly much more e cient than the algorithm presented in Walther (J.

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