A note on the weak Lefschetz property of monomial complete intersections in positive characteristic
Abstract
Let K be an algebraically closed field of characteristic p > 0. We apply a theorem of C. Han to give an explicit description for the weak Lefschetz property of the monomial Artinian complete intersection A = K[X,Y,Z]/(X^d,Y^d,Z^d) in terms of d and p. This answers a question of J. Migliore, R. M. Miro-Roig and U. Nagel and, equivalently, characterizes for which characteristics the rank-2 syzygy bundle Syz(X^d,Y^d,Z^d) on PP^2 satisfies the Grauert-Muelich theorem. As a corollary we obtain that for p=2 the algebra A has the weak Lefschetz property if and only if d=(2^t+1)/3 or d=(2^t-1)/3 for some positive integer t. This was recently conjectured by J. Li and F. Zanello.
Keywords
Cite
@article{arxiv.1003.0824,
title = {A note on the weak Lefschetz property of monomial complete intersections in positive characteristic},
author = {Holger Brenner and Almar Kaid},
journal= {arXiv preprint arXiv:1003.0824},
year = {2010}
}
Comments
10 pages; final version (only minor changes to the previous version); to appear in Collectanea Mathematica