English

Topological obstructions for rational cuspidal curves in Hirzebruch surfaces

Algebraic Geometry 2014-11-04 v2 Geometric Topology

Abstract

We study rational cuspidal curves in Hirzebruch surfaces. We provide two obstructions for the existence of rational cuspidal curves in Hirzebruch surfaces with prescribed types of singular points. The first result comes from Heegaard--Floer theory and is a generalization of a result by Livingston and the first author. The second criterion is obtained by comparing the spectrum of a suitably defined link at infinity of a curve with spectra of its singular points.

Keywords

Cite

@article{arxiv.1410.4464,
  title  = {Topological obstructions for rational cuspidal curves in Hirzebruch surfaces},
  author = {Maciej Borodzik and Torgunn Karoline Moe},
  journal= {arXiv preprint arXiv:1410.4464},
  year   = {2014}
}

Comments

28 pages, 11 figures. v2: Section 3.5 rewritten