Author:
Martín-Morales Jorge,Vos Lena
Abstract
AbstractIn 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.
Publisher
Springer Science and Business Media LLC
Reference28 articles.
1. M. Alberich-Carramiñana, P. Almirón, G. Blanco, A. Melle-Hernández, The minimal Tjurina number of irreducible germs of plane curve singularities. Indiana Univ. Math. J. (to appear)arXiv:1904.02652 (2019)
2. E. Artal Bartolo, J.I. Cogolludo-Agustín, J. Martín-Morales, Cremona transformations of weighted projective planes, Zariski pairs, and rational cuspidal curves, in Singularities and Their Interaction with Geometry and Low Dimensional Topology. Trends in Mathematics (Birkhäuser, Cham, 2021), pp. 117–157
3. E. Artal Bartolo, J. Martín-Morales, J. Ortigas-Galindo, Cartier and Weil divisors on varieties with quotient singularities. Int. J. Math. 25(11), 1450100, 20 (2014)
4. E. Artal Bartolo, J. Martín-Morales, J. Ortigas-Galindo, Intersection theory on abelian-quotient $$V$$-surfaces and $$\mathbb{Q} $$-resolutions. J. Singul. 8, 11–30 (2014)
5. G. Blanco. Yano’s conjecture. Invent. Math. (2021)