Semigroups, d-invariants and deformations of cuspidal singular points of plane curves
Algebraic Geometry
2016-09-15 v2 Geometric Topology
Abstract
We apply Heegaard Floer homology to study deformations of singularities of plane algebraic curves. Our main result provides an obstruction to the existence of a deformation between two singularities. Generalizations include the case of multiple singularities. The obstruction is formulated in terms of a semicontinuity property for semigroups associated to the singularities.
Keywords
Cite
@article{arxiv.1305.2868,
title = {Semigroups, d-invariants and deformations of cuspidal singular points of plane curves},
author = {Maciej Borodzik and Charles Livingston},
journal= {arXiv preprint arXiv:1305.2868},
year = {2016}
}
Comments
v2. 20 pages. Minor revision. Added comparison of the semigroup semicontinuity with a criterion obtained from the upsilon function of Ozsvath, Szabo and Stipsicz