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In this article, we consider an infinite family of normal surfacesingularities with an integral homology sphere link which is related to thefamily of space monomial curves with a plane semigroup. These monomial curvesappear as the special fibers of equisingular families of curves whose genericfibers are a complex plane branch, and the related surface singularities appearin a proof of the monodromy conjecture for these curves. To investigate whetherthe link of a normal surface singularity is an integral homology sphere, onecan use a characterization that depends on the determinant of the intersectionmatrix of a (partial) resolution. To study our family, we apply thischaracterization with a partial toric resolution of our singularitiesconstructed as a sequence of weighted blow-ups.

Normal surface singularities with an integral homology sphere link related to space monomial curves with a plane semigroup