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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Parametrization of rational maps on a variety of general type, and the finiteness theorem


Authors: Lucio Guerra and Gian Pietro Pirola
Journal: Proc. Amer. Math. Soc. 142 (2014), 93-100
MSC (2010): Primary 14E05, 14N05
Published electronically: September 27, 2013
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Abstract: In a previous paper we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing the natural parametrization of maps by means of the space of linear projections in a suitable projective space, and this leads to some new insight into the geometry of the finiteness theorem.


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Additional Information

Lucio Guerra
Affiliation: Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italia
Email: lucio.guerra@unipg.it

Gian Pietro Pirola
Affiliation: Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italia
Email: gianpietro.pirola@unipv.it

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11750-8
PII: S 0002-9939(2013)11750-8
Keywords: Rational maps, pluricanonical maps, varieties of general type, canonical volume
Received by editor(s): October 17, 2011
Received by editor(s) in revised form: March 2, 2012
Published electronically: September 27, 2013
Communicated by: Lev Borisov
Article copyright: © Copyright 2013 American Mathematical Society