论文标题
意想不到的斯坦因填充物，理性的表面奇点和平面曲线排列
Unexpected Stein fillings, rational surface singularities, and plane curve arrangements
论文作者
论文摘要
我们将Stein填充物和Milnor纤维的理性表面奇异性与基本周期降低进行比较。 De Jong-Van Straten在[DJVS98]中研究了这类奇异性的变形理论。它们将奇异平面曲线的细菌与每个奇异性相关联，并通过此奇异曲线的变形描述了Milnor纤维。我们考虑表面奇点的联系，配备了其规范接触结构，并开发了De Jong-Van Straten结构的符合性类似物。使用平面开放书籍和Lefschetz纤维纤维，我们通过某些互合磁盘的安排来描述链接的所有施坦填充物，这是通过与奇异性的平面曲线胚芽的同质拷贝有关的。结果，我们表明，该类的许多理性概念都承认，斯坦因填充物与任何米尔诺纤维都没有很大的差异。这与先前已知的情况（例如简单和商的表面奇点）形成鲜明对比，其中已知Milnor纤维会产生所有Stein填充物。另一方面，我们表明，如果为了减少基本周期的奇异性，那么每个特殊曲线的自我讲义最多在最小分辨率中为-5，那么该链接具有独特的Stein填充（由Milnor纤维给出）。
We compare Stein fillings and Milnor fibers for rational surface singularities with reduced fundamental cycle. Deformation theory for this class of singularities was studied by de Jong-van Straten in [dJvS98]; they associated a germ of a singular plane curve to each singularity and described Milnor fibers via deformations of this singular curve. We consider links of surface singularities, equipped with their canonical contact structures, and develop a symplectic analog of de Jong-van Straten's construction. Using planar open books and Lefschetz fibrations, we describe all Stein fillings of the links via certain arrangements of symplectic disks, related by a homotopy to the plane curve germ of the singularity. As a consequence, we show that many rational singularities in this class admit Stein fillings that are not strongly diffeomorphic to any Milnor fibers. This contrasts with previously known cases, such as simple and quotient surface singularities, where Milnor fibers are known to give rise to all Stein fillings. On the other hand, we show that if for a singularity with reduced fundamental cycle, the self-intersection of each exceptional curve is at most -5 in the minimal resolution, then the link has a unique Stein filling (given by a Milnor fiber).
