“School of Mathematics”
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| Paper IPM / M / 729 |
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Let Z be a subset of the spectrum of a local ring R stable under specialization and let N be a d-dimensional finitely
generated R-module. It is shown that HZd(N), the d-th local cohomology module of the sheaf associated to N with support in Z, vanishes if and only if for every d-dimensional \fp ∈ \TAss∧R ∧N, there is a \fq ∈ Z such that dim∧R/(\fq∧R+\fp) > 0. Applying this criterion for vanishing of HZd (N), several connectedness results for certain
algebraic varieties are proved.
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