Extremal behaviour in sectional matrices
Commutative Algebra
2017-10-20 v4 Algebraic Geometry
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.
Cite
@article{arxiv.1702.03292,
title = {Extremal behaviour in sectional matrices},
author = {Anna Maria Bigatti and Elisa Palezzato and Michele Torielli},
journal= {arXiv preprint arXiv:1702.03292},
year = {2017}
}