Local cohomology with support in ideals of maximal minors
Abstract
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(sr)+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.
 Publication:

arXiv eprints
 Pub Date:
 October 2011
 DOI:
 10.48550/arXiv.1110.1095
 arXiv:
 arXiv:1110.1095
 Bibcode:
 2011arXiv1110.1095W
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 13D45;
 13C40;
 13C05;
 13A50
 EPrint:
 15 pages. Clarifications added and typos corrected