Hilbert-Kunz functions of cubic curves and surfaces
alg-geom
2008-02-03 v1 Commutative Algebra
Algebraic Geometry
Abstract
We determine the Hilbert-Kunz function of plane elliptic curves in odd characteristic, as well as over arbitrary fields the generalized Hilbert-Kunz functions of nodal cubic curves. Together with results of K. Pardue and P. Monsky, this completes the list of Hilbert-Kunz functions of plane cubics. Combining these results with the calculation of the (generalized) Hilbert-Kunz function of Cayley's cubic surface, it follows that in each degree and over any field of positive characteristic there are curves resp. surfaces taking on the minimally possible Hilbert-Kunz multiplicity.
Cite
@article{arxiv.alg-geom/9610009,
title = {Hilbert-Kunz functions of cubic curves and surfaces},
author = {Ragnar-Olaf Buchweitz and Qun Chen},
journal= {arXiv preprint arXiv:alg-geom/9610009},
year = {2008}
}
Comments
LaTex 2e with Xy-pic v3.2 for commutative diagrams