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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geprüft am 18.05.2024
