On the structure of the Sally module and the second normal Hilbert coefficient

Masuti, Shreedevi; Ozeki, Kazuho; Rossi, Maria Evelina; Truong, Hoang

doi:10.1090/proc/14839

On the structure of the Sally module and the second normal Hilbert coefficient
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by Shreedevi K. Masuti, Kazuho Ozeki, Maria Evelina Rossi and Hoang Le Truong

Proc. Amer. Math. Soc. 148 (2020), 2757-2771

DOI: https://doi.org/10.1090/proc/14839

Published electronically: April 14, 2020

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Abstract:

The Hilbert coefficients of the normal filtration give important geometric information on the base ring like the pseudo-rationality. The Sally module was introduced by W.V. Vasconcelos and it is useful to connect the Hilbert coefficients to the homological properties of the associated graded module of a Noetherian filtration. In this paper we give a complete structure of the Sally module in the case the second normal Hilbert coefficient attains almost minimal value in an analytically unramified Cohen-Macaulay local ring. As a consequence, in this case we present a complete description of the Hilbert function of the associated graded ring of the normal filtration. A deep analysis of the vanishing of the third normal Hilbert coefficient has been necessary. This study is related to a longstanding conjecture stated by S. Itoh.

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