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