Linear systems of rational curves on rational surfaces
Algebraic Geometry
2012-02-28 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1202.5889,
title = {Linear systems of rational curves on rational surfaces},
author = {Daniel Daigle and Alejandro Melle Hernandez},
journal= {arXiv preprint arXiv:1202.5889},
year = {2012}
}