Computing the support of local cohomology modules

Details Computing the support of local cohomology modules Computing the support of local cohomology modules

2006-06-06

arxiv.org/abs/math/0606142v2

Mathematics

Algebraic Geometry

15 pages

Scientific paper

For a polynomial ring $R=k[x_1,...,x_n]$, we present a method to compute the characteristic cycle of the localization $R_f$ for any nonzero polynomial $f\in R$ that avoids a direct computation of $R_f$ as a $D$-module. Based on this approach, we develop an algorithm for computing the characteristic cycle of the local cohomology modules $H^r_I(R)$ for any ideal $I\subseteq R$ using the \v{C}ech complex. The algorithm, in particular, is useful for answering questions regarding vanishing of local cohomology modules and computing Lyubeznik numbers. These applications are illustrated by examples of computations using our implementation of the algorithm in Macaulay~2.

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