2000/11/22 by Josep Alvarez Montaner, Montaner, Josep Alvarez, Ricardo Garcia Lopez +3
Mathematics · #13D45 (Primary) 32C38 (Secondary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13D45 #msc:32C38
paper · pdf · doi:10.48550/arxiv.math/0011181
24 pages, LaTeX2e
arxiv created 2000/11/22 · arxiv updated 2009/11/30
Let k be a field of characteristic zero and I an ideal defining an arrangement of linear subspaces in the affine space Ank. We compute the D-module theoretic characteristic cycle of the local cohomology modules HrI(k[x1,...,xn]) in terms of the poset defined by the arrangement. In case I is a monomial ideal, we relate the multiplicities of the characteristic cycle with the Betti numbers of the Alexander dual ideal of I, we also study some extension problems attached to the modules HrI(k[x1,...,xn]). If k is the field of complex numbers we study the ubiquity of these local cohomology modules in the category of perverse sheaves in Ank with respect to the stratification given by the coordinate hyperplanes.