论文标题
关于$ \ Mathcal {M} _ {g，n} $的压实
On compactifications of $\mathcal{M}_{g,n}$ with colliding markings
论文作者
论文摘要
在本文中，我们研究了构建模量空间的模块化压实的所有方法，$ \ mathcal {m} _ {g，n} $ $ n $的$ point $ g $的平滑代数曲线，通过允许标记碰撞。我们发现，对于任何这样的压缩，标记的碰撞都由我们称为碰撞复合物的简单复合物控制。相反，我们将$ \ Mathcal {M} _ {g，n} $的模块化压缩具有基本任意的碰撞复合物，其中包括与任何加权指向稳定曲线的任何空间相关的复合物。这些模量空间通过节点曲线和$ \ Mathcal {m} _ {M} _ {M} _ {1，N}的模块化压实对$ \ Mathcal {M} _ {M} _ {G，N} $的模块化压缩进行了分类。这些压缩概括了Hassett，Smyth和Bozlee-Kuo-neff的先前结构。
In this paper, we study all ways of constructing modular compactifications of the moduli space $\mathcal{M}_{g,n}$ of $n$-pointed smooth algebraic curves of genus $g$ by allowing markings to collide. We find that for any such compactification, collisions of markings are controlled by a simplicial complex which we call the collision complex. Conversely, we identify modular compactifications of $\mathcal{M}_{g,n}$ with essentially arbitrary collision complexes, including complexes not associated to any space of weighted pointed stable curves. These moduli spaces classify the modular compactifications of $\mathcal{M}_{g,n}$ by nodal curves with smooth markings as well as the modular compactifications of $\mathcal{M}_{1,n}$ with Gorenstein curves and smooth markings. These compactifications generalize previous constructions given by Hassett, Smyth, and Bozlee--Kuo--Neff.
