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arXiv · 1702.03292

Extremal behaviour in sectional matrices

Anna Maria Bigatti·Elisa Palezzato·Michele Torielli
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Abstract

In this paper we want to revive 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 and Persistence Theorem, a gen- eralization of Gotzmann's persistence Theorem. This suggests that further investigation of this object might cast a new light in the study of geometric consequences of maximal growth of the Hilbert function.

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Anna Maria Bigatti, Elisa Palezzato, Michele Torielli. 2017-02-10. Extremal behaviour in sectional matrices. https://arxiv.org/abs/1702.03292

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