The structure of the Sally module of integrally closed ideals

2015/10/28 by Ozeki, Kazuho, Rossi, Maria Evelina
#13A30 #13D40 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.08292

Abstract

The first two Hilbert coefficients of a primary ideal play an important role in commutative algebra and in algebraic geometry. In this paper we give a complete algebraic structure of the Sally module of integrally closed ideals I in a Cohen-Macaulay local ring A satisfying the equality e₁(I)=e₀(I)-ℓ_A(A/I)+ℓ_A(I²/QI)+1, where Q is a minimal reduction of I, and e₀(I) and e₁(I) denote the first two Hilbert coefficients of I, respectively the multiplicity and the Chern number of I. This almost extremal value of e₁(I) with respect classical inequalities holds a complete description of the homological and the numerical invariants of the associated graded ring. Examples are given.

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