论文标题
代数编织和编织品种
Algebraic Weaves and Braid Varieties
论文作者
论文摘要
在本手稿中，我们研究辫子品种，一类与阳性辫子相关的仿期代数品种。提出了几种几何构造，包括对辫子品种的某些圆环作用和各自的商的全态符号结构。我们还为编织品种之间的对应关系开发了一个图形演算，并使用这些对应关系来获得辫子品种及其商的有趣分层。结果表明，这些分层的最大图表是全体形态符号结构的指数darboux图表，我们将这些地层与Legendrian链接的精确拉格朗日填充物联系起来。
In this manuscript we study braid varieties, a class of affine algebraic varieties associated to positive braids. Several geometric constructions are presented, including certain torus actions on braid varieties and holomorphic symplectic structures on their respective quotients. We also develop a diagrammatic calculus for correspondences between braid varieties and use these correspondences to obtain interesting stratifications of braid varieties and their quotients. It is shown that the maximal charts of these stratifications are exponential Darboux charts for the holomorphic symplectic structures, and we relate these strata to exact Lagrangian fillings of Legendrian links.
