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Article overview
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Rank-2 syzygy bundles on Fermat curves and an application to Hilbert-Kunz functions | | Daniel Brinkmann
; Almar Kaid
; | | Date: |
3 Oct 2014 | | Abstract: | In this paper we describe the Frobenius pull-backs of the syzygy bundles
$Syz_C(X^a, Y^a, Z^a)$, $a geq 1$, 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 $Omega_{P^2}|_C$ of arbitrary
length and a problem of Brenner regarding primes with strongly semistable
reduction. | | Source: | arXiv, 1410.0872 | | Services: | Forum | Review | PDF | Favorites | |
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