A note on the weak Lefschetz property of monomial complete intersections in positive characteristics

• Autores: Holger Brenner, A. Kaid
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 62, Fasc. 1, 2011, págs. 85-93
• Idioma: español
• DOI: 10.1007/s13348-010-0006-8
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• Resumen

  • Let K be an algebraically closed field of characteristic p > 0. We apply a theorem of 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 Migliore, Miró-Roig and Nagel and, equivalently, characterizes for which characteristics the rank-2 syzygy bundle Syz(X^d, Y^d, Z^d) on {{\mathbb {P}}^2} satisfies the Grauert-Mülich theorem. As a corollary we obtain that for p = 2 the algebra A has the weak Lefschetz property if and only if {d=\lfloor\frac{2^t+1}{3}\rfloor} for some positive integer t. This was recently conjectured by Li and Zanello.