Some algebraic consequences of Green’s hyperplane restriction theorems

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We discuss Green's paper [11] 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 the recent work [19]. 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 contains a new argument, kindly provided to us by M. Green, for Theorems 3 and 4 of [11], since we had found a gap in the original proof of those results during the preparation of this manuscript.

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Copyright 2009 Elsevier B.V. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.jpaa.2009.10.010

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Journal of Pure and Applied Algebra