Rank-2 syzygy bundles on Fermat curves and an application to Hilbert-Kunz functions

Autor(en): Brinkmann, Daniel
Kaid, Almar
Stichwörter: Fermat curve; Frobenius periodicity; Hilbert-Kunz function; Hilbert-series; Mathematics; Projective dimension; Strongly semistable; Syzygy module; Vector bundle
Erscheinungsdatum: 2016
Herausgeber: SPRINGER HEIDELBERG
Journal: BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY
Volumen: 57
Ausgabe: 2
Startseite: 321
Seitenende: 342
Zusammenfassung: 
In this paper we describe the Frobenius pull-backs of the syzygy bundles Syz(C)(X-a, Y-a, Z(a)), a >= 1, on the projective Fermat curve C of degree n in characteristics coprime to n, either by giving their strong Harder-Narasimhan filtration if Syz(C)(X-a, Y-a, Z(a)) is not strongly semistable or in the strongly semistable case by their periodicity behavior. Moreover, we apply these results to Hilbert-Kunz functions, to find Frobenius periodicities of the restricted cotangent bundle Omega(P2 vertical bar C) of arbitrary length and a problem of Brenner regarding primes with strongly semistable reduction.
ISSN: 01384821
DOI: 10.1007/s13366-015-0251-9

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