Computing the support of local cohomology modules

• Autores: Anton Leykin, Josep Àlvarez Montaner
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 12, 2006, págs. 1328-1344
• Idioma: inglés
• DOI: 10.1016/j.jsc.2006.09.001
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• Resumen

  • Abstract For a polynomial ring R=k[x1,¿,xn], we present a method to compute the characteristic cycle of the localization Rf for any nonzero polynomial fR that avoids a direct computation of Rf as a D-module. Based on this approach, we develop an algorithm for computing the characteristic cycle of the local cohomology modules for any ideal IR using the Cech 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.