HilbertKunz functions of cubic curves and surfaces
Abstract
We determine the HilbertKunz function of plane elliptic curves in odd characteristic, as well as over arbitrary fields the generalized HilbertKunz functions of nodal cubic curves. Together with results of K. Pardue and P. Monsky, this completes the list of HilbertKunz functions of plane cubics. Combining these results with the calculation of the (generalized) HilbertKunz 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 HilbertKunz multiplicity.
 Publication:

arXiv eprints
 Pub Date:
 October 1996
 arXiv:
 arXiv:alggeom/9610009
 Bibcode:
 1996alg.geom.10009B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Commutative Algebra;
 11C20;
 13H15;
 14H45
 EPrint:
 LaTex 2e with Xypic v3.2 for commutative diagrams