Severi varieties and self rational maps of K3 surfaces

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.

20 pages

Cited by in corpus (4)

• The geometry of the moduli space of odd spin curves
• Self Rational Maps of K3 Surfaces
• Nodal curves with general moduli on K3 surfaces
• Density of Rational Curves on K3 Surfaces