Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 199 (2010), 43-93.
Birational classification of curves on rational surfaces
In this paper we consider the birational classification of pairs , with a rational surface and a linear system on . We give a classification theorem for such pairs, and we determine, for each irreducible plane curve , its Cremona minimal models, that is, those plane curves which are equivalent to via a Cremona transformation and have minimal degree under this condition.
Nagoya Math. J., Volume 199 (2010), 43-93.
First available in Project Euclid: 14 September 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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)
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