Lefschetz properties and the Veronese construction

Details Lefschetz properties and the Veronese construction Lefschetz properties and the Veronese construction

2011-12-21

arxiv.org/abs/1112.5015v1

Mathematics

Combinatorics

10 pages

Scientific paper

In this paper, we investigate Lefschetz properties of Veronese subalgebras. We show that, for a sufficiently large $r$, the $r$\textsuperscript{th} Veronese subalgebra of a Cohen-Macaulay standard graded $K$-algebra has properties similar to the weak and strong Lefschetz properties, which we call the `almost weak' and `almost strong' Lefschetz properties. By using this result, we obtain new results on $h$- and $g$-polynomials of Veronese subalgebras.

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