On Invariants and Endomorphism Rings of Local Cohomology Modules

2013/10/03 by Mahmood, Waqas, Schenzel, Peter
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.0920

Abstract

Let (R,\mathfrakm) denote an n-dimensional Gorenstein ring. For an ideal I ⊂ R with \grade I = c we define new numerical invariants τ_i,j(I) as the socle dimensions of Hⁱ_\mathfrakm(H^n-j_I(R)). In case of a regular local ring containing a field these numbers coincide with the Lyubeznik numbers λ_i,j(R/I). We use τ_d,d(I), d = dim R/I, to characterize the surjectivity of the natural homomorphism f : R → \Hom_R(H^c_IR(R),H^c_IR(R)). As a technical tool we study several natural homomorphisms. Moreover we prove a few results on τ_i,j(I).

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