Computing the support of local cohomology modules

Josep Àlvarez Montaner; Anton Leykin

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arXiv · math/0606142

Computing the support of local cohomology modules

Josep Àlvarez Montaner·Anton Leykin

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Abstract

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 Čech 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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BibTeX RIS

Josep Àlvarez Montaner, Anton Leykin. 2006-09-19. Computing the support of local cohomology modules. https://arxiv.org/abs/math/0606142

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