Nagoya Mathematical Journal

Birational classification of curves on rational surfaces

Alberto Calabri and Ciro Ciliberto

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Abstract

In this paper we consider the birational classification of pairs SL, 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.

Article information

Source
Nagoya Math. J., Volume 199 (2010), 43-93.

Dates
First available in Project Euclid: 14 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1284471570

Digital Object Identifier
doi:10.1215/00277630-2010-003

Mathematical Reviews number (MathSciNet)
MR2730411

Zentralblatt MATH identifier
1205.14015

Subjects
Primary: 14E05: Rational and birational maps
Secondary: 14J26: Rational and ruled surfaces 14H50: Plane and space curves 14E07: Birational automorphisms, Cremona group and generalizations 14E30: Minimal model program (Mori theory, extremal rays)

Citation

Calabri, Alberto; Ciliberto, Ciro. Birational classification of curves on rational surfaces. Nagoya Math. J. 199 (2010), 43--93. doi:10.1215/00277630-2010-003. https://projecteuclid.org/euclid.nmj/1284471570


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