Mathematical Research Letters
Volume 19 (2012)
Lefschetz properties and the Veronese construction
Pages: 1043 – 1053
In this paper, we investigate Lefschetz properties of Veronese subalgebras. We show that, for a sufficiently large $r$, the $r$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 ‘quasi-weak’ and ‘almost strong’ Lefschetz properties. By using this result, we obtain new results on $h$- and $g$-polynomials of Veronese subalgebras.