Linear systems of rational curves on rational surfaces

Details Linear systems of rational curves on rational surfaces Linear systems of rational curves on rational surfaces

2012-02-27

arxiv.org/abs/1202.5889v1

Mathematics

Algebraic Geometry

Scientific paper

Given a curve C on a projective nonsingular rational surface S, over an algebraically closed field of characteristic zero, we are interested in the set Omega_C of linear systems Lambda on S satisfying C is in Lambda, dim Lambda > 0, and the general member of Lambda is a rational curve. The main result of the paper gives a complete description of Omega_C and, in particular, characterizes the curves C for which Omega_C is non empty.

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