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

2001/03/02 by Uli Walther, Walther, Uli
Computer Science · Mathematics · #14F40 #14Q15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.math/0103013

openalex publication_date 2001/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Gröbner 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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