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Birational classification of curves on rational surfaces

Published online by Cambridge University Press:  11 January 2016

Alberto Calabri  and
Ciro Ciliberto
Alberto Calabri
Affiliation:
Dipartimento di Matematica, Università degli Studi di Ferrara, 44121 Ferrara, Italy, alberto.calabri@unife.it
Ciro Ciliberto
Affiliation:
Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”, 00133 Roma, Italy, cilibert@mat.uniroma2.it
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Abstract

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In this paper we consider the birational classification of pairs (S, ℒ), with S a rational surface and ℒ a linear system on S. We give a classification theorem for such pairs, and we determine, for each irreducible plane curve B, its Cremona minimal models, that is, those plane curves which are equivalent to B via a Cremona transformation and have minimal degree under this condition.

Keywords

14E0514J2614H5014E0714E30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 199 , September 2010 , pp. 43 - 93
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

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