Mathematics – Algebraic Geometry
Scientific paper
2010-11-18
Mathematics
Algebraic Geometry
Scientific paper
In this note we show that the restriction of the cotangent bundle $\Omega_{\mathbb P}^2$ of the projective plane to a Fermat curve $C$ of degree $d$ in characteristic $p \equiv -1 \mod 2d$ is, up to tensoration with a certain line bundle, isomorphic to its Frobenius pull-back. This leads to a Frobenius periodicity $F^*({\mathcal E}) \cong {\mathcal E} $ on the Fermat curve of degree $2d$, where ${\mathcal E}= {\rm Syz}(U^2,V^2,W^2)(3)$.
Brenner Holger
Kaid Almar
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