Local Cohomology and Group Actions.

Local Cohomology;Determinantal Ideals;Ideals of Maximal Minors;Mathematics;Science;Mathematics

Witt, Emily ElspethZhang, Wenliang ;

University of Michigan

关键词: Local Cohomology;    Determinantal Ideals;    Ideals of Maximal Minors;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/86460/emwitt_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Suppose that k is a field of characteristic zero, X is an r by s matrix of indeterminates, where r is less than or equal to s, and R = k[X] is the polynomial ring over k in the entries of X.We study the local cohomology modules of R with support in I, 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 these local cohomology modules at the highest nonvanishing index, i = r(s-r) +1, and characterize all nonzero ones as submodules of certain indecomposable injective modules.We also calculate certain iterated local cohomology modules in the case that r = 2.These results are consequences of more general theorems regarding linearly reductive groups acting on local cohomology modules of polynomial rings.