Linear systems associated to unicuspidal rational plane curves
Algebraic Geometry
2012-02-29 v1
Abstract
A curve C in the projective plane is called non-negative if the self-intersection number of C after the minimal resolution of singularities of C is non-negative. Given a unicuspidal rational plane curve C with singular point P, we study the unique pencil Lambda_C on the projective plane satisfying C is in Lambda_C and P is its unique base point. We show that the general member of Lambda_C is a rational curve if and only if the curve C is non-negative. We also show that in such a case then Lambda_C has a dicritical of degree 1. Note that all currently known unicuspidal rational curves C in the projective plane are non-negative.
Cite
@article{arxiv.1202.6146,
title = {Linear systems associated to unicuspidal rational plane curves},
author = {Daniel Daigle and Alejandro Melle Hernández},
journal= {arXiv preprint arXiv:1202.6146},
year = {2012}
}