Normal surface singularities with an integral homology sphere link related to space monomial curves with a plane semigroup
Abstract
In this article, we consider an infinite family of normal surface singularities with an integral homology sphere link which is related to the family of space monomial curves with a plane semigroup. These monomial curves appear as the special fibers of equisingular families of curves whose generic fibers are a complex plane branch, and the related surface singularities appear in a proof of the monodromy conjecture for these curves. To investigate whether the link of a normal surface singularity is an integral homology sphere, one can use a characterization that depends on the determinant of the intersection matrix of a (partial) resolution. To study our family, we apply this characterization with a partial toric resolution of our singularities constructed as a sequence of weighted blow-ups.
Keywords
Cite
@article{arxiv.2008.10918,
title = {Normal surface singularities with an integral homology sphere link related to space monomial curves with a plane semigroup},
author = {Jorge Martín-Morales and Lena Vos},
journal= {arXiv preprint arXiv:2008.10918},
year = {2020}
}
Comments
v2: 31 pages; Section 3.3 was added to answer Jonathan Wahl's question on the possible connection with the singularities of splice type, introduction and preliminary section were changed accordingly, minor typos and aesthetic changes