Severi varieties and self rational maps of K3 surfaces
Algebraic Geometry
2010-09-20 v1
Abstract
Self-rational maps of generic algebraic K3 surfaces are conjectured to be trivial. We relate this conjecture to a conjecture concerning the irreducibility of the universal Severi varieties parametrizing nodal curves of given genus and degree lying on some K3 surface. We also establish a number of numerical constraints satisfied by such non trivial rational maps, that is of topological degree >1.
Keywords
Cite
@article{arxiv.0704.3163,
title = {Severi varieties and self rational maps of K3 surfaces},
author = {Thomas Dedieu},
journal= {arXiv preprint arXiv:0704.3163},
year = {2010}
}
Comments
20 pages