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On the finiteness theorem for rational maps on a variety of general type

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Abstract

The dominant rational maps of finite degree from a fixed variety to varieties of general type, up to birational isomorphisms, form a finite set. This has been known as the Iitaka-Severi conjecture, and is nowdays an established result, in virtue of some recent advances in the theory of pluricanonical maps. We study the question of finding some effective estimate for the finite number of maps, and to this aim we provide some update and refinement of the classical treatment of the subject.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123, Perugia, Italia

    Lucio Guerra

  2. Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100, Pavia, Italia

    Gian Pietro Pirola

Authors
  1. Lucio Guerra
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  2. Gian Pietro Pirola
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Correspondence to Lucio Guerra.

Additional information

The first author is partially supported by: Finanziamento Ricerca di Base 2007 Univ. Perugia.

The second author is partially supported by: 1) PRIN 2007 “Spazi di moduli e teorie di Lie”; 2) Indam (GNSAGA); 3) FAR 2006 (PV): “Varietà algebriche, calcolo algebrico, grafi orientati e topologici”.

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Guerra, L., Pirola, G.P. On the finiteness theorem for rational maps on a variety of general type. Collect. Math. 60, 261–276 (2009). https://doi.org/10.1007/BF03191371

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  • DOI: https://doi.org/10.1007/BF03191371

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