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SEVERI VARIETIES AND SELF-RATIONAL MAPS OF K3 SURFACES

THOMAS DEDIEU

Université Pierre et Marie Curie – Paris 6, Institut de Mathématiques de Jussieu (UMR 7586), Équipe de Topologie et Géométrie Algébriques, 175 rue du Chevaleret, 75013 Paris, France

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https://doi.org/10.1142/S0129167X09005844Cited by:8 (Source: Crossref)

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 parameterizing nodal curves of given genus and degree lying on some K3 surface. We also establish a number of numerical constraints satisfied by such nontrivial rational maps, that is of topological degree > 1.

Keywords:

AMSC: 14J28, 14E05, 14C05

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