Extremal behavior in sectional matrices

Anna Bigatti; Elisa Palezzato; Michele Torielli

doi:10.1142/S0219498819500415

Extremal behavior in sectional matrices

Anna Bigatti, Elisa Palezzato, Michele Torielli

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, we recall the object sectional matrix which encodes the Hilbert functions of successive hyperplane sections of a homogeneous ideal. We translate and/or reprove recent results in this language. Moreover, some new results are shown about their maximal growth, in particular, a new generalization of Gotzmann's Persistence Theorem, the presence of a GCD for a truncation of the ideal, and applications to saturated ideals.

Original language	English (US)
Article number	1950041
Journal	Journal of Algebra and Its Applications
Volume	18
Issue number	3
DOIs	https://doi.org/10.1142/S0219498819500415
State	Published - Mar 1 2019
Externally published	Yes

Keywords

extremal behavior
generic initial ideal
Hilbert function
hyperplane section
reduction number
Sectional matrix

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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AU - Torielli, Michele

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AB - In this paper, we recall the object sectional matrix which encodes the Hilbert functions of successive hyperplane sections of a homogeneous ideal. We translate and/or reprove recent results in this language. Moreover, some new results are shown about their maximal growth, in particular, a new generalization of Gotzmann's Persistence Theorem, the presence of a GCD for a truncation of the ideal, and applications to saturated ideals.

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KW - generic initial ideal

KW - Hilbert function

KW - hyperplane section

KW - reduction number

KW - Sectional matrix

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Extremal behavior in sectional matrices

Abstract

Keywords

ASJC Scopus subject areas

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