论文标题
正常的表面奇异性具有与空间单曲线相关的积分同源球形链接与平面半群
Normal surface singularities with an integral homology sphere link related to space monomial curves with a plane semigroup
论文作者
论文摘要
在本文中，我们考虑了具有正常表面奇异性的无限家族，具有积分同源性球形链接，该链接与平面半群有关空间单曲线曲线的家族。这些单曲线显示为曲线的曲线的特殊纤维，其通用纤维是一个复杂的平面分支，相关的表面奇异性出现在这些曲线的单层猜想的证据中。为了研究正常表面奇点的链接是否是一个积分同源性球体，可以使用取决于（部分）分辨率的相交矩阵的决定因素的表征。为了研究我们的家庭，我们将这种特征应用于构造的一系列加权爆炸序列的部分复曲面。
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.
