English

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}
}
R2 v1 2026-06-21T20:25:31.717Z