Algorithmic Determination of the Rational Cohomology of Complex Varieties via Differential Forms

Details Algorithmic Determination of the Rational Cohomology of Complex Varieties via Differential Forms Algorithmic Determination of the Rational Cohomology of Complex Varieties via Differential Forms

2001-03-02

arxiv.org/abs/math/0103013v1

Mathematics

Algebraic Geometry

amslatex, 22 pages. Uses diagrams.sty

Scientific paper

We give algorithms for the computation of the algebraic de Rham cohomology of open and closed algebraic sets inside projective space or other smooth complex toric varieties. The methods, which are based on Gr\"obner basis computations in rings of differential operators, can also be used to compute the cohomology of intersections of smooth closed and open subsets, and in certain situations the cup-product structure. We give some examples which were carried out with the help of \Mtwo.

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