Birational classification of curves on rational surfaces

Details Birational classification of curves on rational surfaces Birational classification of curves on rational surfaces

2009-06-26

arxiv.org/abs/0906.4963v1

Mathematics

Algebraic Geometry

33 pages

Scientific paper

In this paper we consider the birational classification of pairs (S,L), with
S a rational surfaces 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, i.e. those plane curves which are equivalent to B
via a Cremona transformation, and have minimal degree under this condition.

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