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arXiv · 0907.3912

Some algebraic consequences of Green's hyperplane restriction theorems

Mats Boij·Fabrizio Zanello
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Abstract

We discuss a paper of M. Green from a new algebraic perspective, and provide applications of its results to level and Gorenstein algebras, concerning their Hilbert functions and the weak Lefschetz property. In particular, we will determine a new infinite class of symmetric $h$-vectors that cannot be Gorenstein $h$-vectors, which was left open in a recent work of Migliore-Nagel-Zanello. This includes the smallest example previously unknown, $h=(1,10,9,10,1)$. As M. Green's results depend heavily on the characteristic of the base field, so will ours. The appendix will contain a new argument, kindly provided to us by M. Green, for Theorems 3 and 4 of his paper, since we had found a gap in the original proof of those results during the preparation of this manuscript.

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Mats Boij, Fabrizio Zanello. 2009-10-09. Some algebraic consequences of Green's hyperplane restriction theorems. https://arxiv.org/abs/0907.3912

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