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Acta Mathematica Vietnamica

“Infinite” Properties of Certain Local Cohomology Modules of Determinantal Rings

icon-email Peter Schenzel

Abstract

For given integers m,n2 there are examples of ideals I of complete determinantal local ring (R,m), dimR=m+n1, gradeI=n1, with the canonical module ωR and the property that the socle dimensions of HIm+n2(ωR) and Hmm(HIn1(ωR)) are not finite. In the case of m=n, i.e., a Gorenstein ring, the socle dimensions provide further information about the τ-numbers as studied in Mahmood and Schenzel (J. Algebra 372, 56–67, 10). Moreover, the endomorphism ring of HIn1(ωR) is studied and shown to be an R-algebra of finite type but not finitely generated as R-module generalizing an example of Schenzel (J. Algebra 344, 229–245, 15).