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arXiv · 0704.3163

Severi varieties and self rational maps of K3 surfaces

Thomas Dedieu
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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.

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Thomas Dedieu. 2007-04-24. Severi varieties and self rational maps of K3 surfaces. https://arxiv.org/abs/0704.3163

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