Severi varieties and self rational maps of K3 surfaces

Details Severi varieties and self rational maps of K3 surfaces Severi varieties and self rational maps of K3 surfaces

2007-04-24

arxiv.org/abs/0704.3163v1

Internat. J. Math., 20(12): 1455-1477, 2009

Mathematics

Algebraic Geometry

20 pages

Scientific paper

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.

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