论文标题
温斯坦的把手，用于平滑复曲面的补充
Weinstein handlebodies for complements of smoothed toric divisors
论文作者
论文摘要
我们研究了复曲面歧管与温斯坦手柄之间的相互作用。我们在Delzant多层室上定义了以部分为中心的条件，我们证明，该条件可确保相应的曲面分裂部分平滑的补体支持明确的Weinstein结构。许多失败此情况的例子也无法使温斯坦（甚至精确）与部分平滑的除数相互补充。我们研究了实现这种韦恩斯坦领域补充的Delzant多型的组合可能性。我们还开发了一种算法，以构建GOMPF标准形式的Weinstein Handerby图，以构造这种部分平滑的曲折除法。我们通常开发的算法会为任何Weinstein Handleby图输出，以适用于任何Weinstein 4 manifold，它们通过将2个手柄连接到任何表面$ F $的磁盘cotangengent束，其中2柄沿着$ f $上的曲线的共同导向的共晶型凸起。我们讨论如何使用这些图来计算不变性，并提供许多应用此过程的示例。例如，我们为$ \ mathbb {cp}^2 $中的平滑和节点立方体的补充提供Weinstein Handlebody图。
We study the interactions between toric manifolds and Weinstein handlebodies. We define a partially-centered condition on a Delzant polytope, which we prove ensures that the complement of a corresponding partial smoothing of the toric divisor supports an explicit Weinstein structure. Many examples which fail this condition also fail to have Weinstein (or even exact) complement to the partially smoothed divisor. We investigate the combinatorial possibilities of Delzant polytopes that realize such Weinstein domain complements. We also develop an algorithm to construct a Weinstein handlebody diagram in Gompf standard form for the complement of such a partially smoothed toric divisor. The algorithm we develop more generally outputs a Weinstein handlebody diagram for any Weinstein 4-manifold constructed by attaching 2-handles to the disk cotangent bundle of any surface $F$, where the 2-handles are attached along the co-oriented conormal lifts of curves on $F$. We discuss how to use these diagrams to calculate invariants and provide numerous examples applying this procedure. For example, we provide Weinstein handlebody diagrams for the complements of the smooth and nodal cubics in $\mathbb{CP}^2$.
