Local cohomology with support in ideals of maximal minors

Details Local cohomology with support in ideals of maximal minors Local cohomology with support in ideals of maximal minors

2011-10-05

arxiv.org/abs/1110.1095v2

Mathematics

Commutative Algebra

15 pages. Clarifications added and typos corrected

Scientific paper

Suppose that k is a field of characteristic zero, X is an r by s matrix of indeterminates, where r \leq s, and R = k[X] is the polynomial ring over k in the entries of X. We study the local cohomology modules H^i_I(R), where I is the ideal of R generated by the maximal minors of X. We identify the indices i for which these modules vanish, compute H^i_I(R) at the highest nonvanishing index, i = r(s-r)+1, and characterize all nonzero ones as submodules of certain indecomposable injective modules. These results are consequences of more general theorems regarding linearly reductive groups acting on local cohomology modules of polynomial rings.

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