The first two Hilbert coecients 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/I) + l(I2/QI) + 1 where Q is a minimal reduction of I, and e0(I) and e1(I) denote the rst two Hilbert coecients of I; respectively, the multiplicity and the Chern number of I. This almost extremal value of e1(I) with respect to classical inequalities holds a complete description of the homological and the numerical invariants of the associated graded ring. Examples are given.
The structure of the Sally module of integrally closed ideals
ROSSI, MARIA EVELINA
2017-01-01
Abstract
The first two Hilbert coecients 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/I) + l(I2/QI) + 1 where Q is a minimal reduction of I, and e0(I) and e1(I) denote the rst two Hilbert coecients of I; respectively, the multiplicity and the Chern number of I. This almost extremal value of e1(I) with respect to 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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