Mathematical Research Letters

Volume 19 (2012)

Number 5

Lefschetz properties and the Veronese construction

Pages: 1043 – 1053



Martina Kubitzke (Institut für Mathematik, Goethe-Universität, Frankfurt am Main, Germany)

Satoshi Murai (Department of Mathematical Science, Yamaguchi University, Yamaguchi, Japan)


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.

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