论文标题
从投影辫子布置中建造平面多边形空间
Building planar polygon spaces from the projective braid arrangement
论文作者
论文摘要
具有通用侧长的平面多边形的模量空间是平滑的封闭歧管。众所周知，这些歧管包含射影线上不同点的模量空间的真实点，作为开放密集的子集。因此，这种多边形空间是对这个真实模量空间的压缩。卡普拉诺夫（Kapranov）表明，可以通过沿最小的建筑集沿迭代的炸毁，可以从$ a $ a $ a $ a $（等效地，投射辫子布置）的投射coxeter综合体中获得磨难 - 穆福德 - 克纳森紧凑型的真实点。在本文中，我们表明，这些平面多边形空间也可以从$ $ a $的投影coxeter综合体中获得，并通过沿最小建筑集的子收集进行迭代的蜂窝手术。有趣的是，该子收集由与称为遗传密码的长度向量相关的组合数据确定。
The moduli space of planar polygons with generic side lengths is a smooth, closed manifold. It is known that these manifolds contain the real points of the moduli space of distinct points on the projective line as an open dense subset. Hence, such a polygon space is a compactification of this real moduli space. Kapranov showed that the real points of the Deligne-Mumford-Knudson compactification can be obtained from the projective Coxeter complex of type $A$ (equivalently, the projective braid arrangement) by iteratively blowing up along the minimal building set. In this paper we show that these planar polygon spaces can also be obtained from the projective Coxeter complex of type $A$ by performing an iterative cellular surgery along a sub-collection of the minimal building set. Interestingly, this sub-collection is determined by the combinatorial data associated with the length vector called the genetic code.
