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

Autor(en): Brenner, Holger 
Kaid, Almar
Stichwörter: Artinian algebra; Grauert-Mulich Theorem; Mathematics; Mathematics, Applied; Monomial complete intersection; Stable bundle; Syzygy; SYZYGY BUNDLES; Weak Lefschetz property
Erscheinungsdatum: 2011
Herausgeber: SPRINGER
Journal: COLLECTANEA MATHEMATICA
Volumen: 62
Ausgabe: 1
Startseite: 85
Seitenende: 93
Zusammenfassung: 
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, Miro-Roig and Nagel and, equivalently, characterizes for which characteristics the rank-2 syzygy bundle Syz(X(d), Y (d), Z(d)) on P(2) satisfies the Grauert-Mulich theorem. As a corollary we obtain that for p = 2 the algebra A has the weak Lefschetz property if and only if d = left perpendicular2(t)+1/3right perpendicular for some positive integer t. This was recently conjectured by Li and Zanello.
ISSN: 00100757
DOI: 10.1007/s13348-010-0006-8

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