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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geprüft am 19.05.2024