论文标题
log symbletectic歧管的本地torelli定理
A local Torelli theorem for log symplectic manifolds
论文作者
论文摘要
我们建立了一个与对数杆的全体形态符号结构的模量空间的局部模型，其极性除数是正常的横断面。与没有电线的情况相反，模量空间是单数的：当符号结构的同时学类别满足具有整数系数的某些线性方程时，其极性除数可以在部分平滑的模量空间中得到部分平滑，以使可能与非固定交叉结构相对应。这些组件是由我们称为平滑图的组合数据索引的，并且可以适合算法分类。将理论应用于四维投影空间，我们总共获得了40个模量空间的不可还原组成部分，其中大多数是新的。我们的主要技术是对相关变形复合物（Poisson协同学）作为可构造衍生类别的对象的详细分析。
We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. In contrast to the case without poles, the moduli space is singular: when the cohomology class of a symplectic structure satisfies certain linear equations with integer coefficients, its polar divisor can be partially smoothed, yielding adjacent irreducible components of the moduli space that correspond to possibly non-normal crossings structures. These components are indexed by combinatorial data we call smoothing diagrams, and amenable to algorithmic classification. Applying the theory to four-dimensional projective space, we obtain a total of 40 irreducible components of the moduli space, most of which are new. Our main technique is a detailed analysis of the relevant deformation complex (the Poisson cohomology) as an object of the constructible derived category.
