Some algebraic consequences of Green’s hyperplane restriction theorems
We discuss Green's paper  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 . 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 , since we had found a gap in the original proof of those results during the preparation of this manuscript.
Journal of Pure and Applied Algebra
Some algebraic consequences of Green’s hyperplane restriction theorems.
Journal of Pure and Applied Algebra,
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