论文标题
射影平面中点和线模量的压缩
Compactifications of moduli of points and lines in the projective plane
论文作者
论文摘要
投影二元性标识模量空间$ \ mathbf {b} _n $和$ \ mathbf {x}（x}（3，n）$参数化$ n $ points $ n $ poction的$ \ mathbb {p}^2 $和$ n $ in diual $ $ \ mathbbbb {p Mathbbbb {p Mathbbbb {p Mathbb {p} $ \ mathbb {p}^$的线性n $ points $ n $ quottion $ n $ quotter。空间$ \ mathbf {x}（3，n）$接纳了卡普拉诺夫（Kapranov）的Chow商人紧凑型$ \ overline {\ Mathbf {x}}（3，n）$，也由Lafforgue，Hacking，Hacking，Keel，Tevelev，Tevelev，Tevelev和Alexeev和Alexeev进行了研究，以提供某些ksba Moduli Specce的典范$ \ mathbb {p}^2 $的退化，带有$ n $“破碎行”。 Gerritzen和Piwek提出了一个双重视角，这是一个紧凑的模量空间，参数$ \ Mathbb {p}^2 $具有$ n $ speepar Points的某些还原变性。我们研究了这些方法之间的关系，回答了2003年卡普拉诺夫的问题。
Projective duality identifies the moduli spaces $\mathbf{B}_n$ and $\mathbf{X}(3,n)$ parametrizing linearly general configurations of $n$ points in $\mathbb{P}^2$ and $n$ lines in the dual $\mathbb{P}^2$, respectively. The space $\mathbf{X}(3,n)$ admits Kapranov's Chow quotient compactification $\overline{\mathbf{X}}(3,n)$, studied also by Lafforgue, Hacking, Keel, Tevelev, and Alexeev, which gives an example of a KSBA moduli space of stable surfaces: it carries a family of certain reducible degenerations of $\mathbb{P}^2$ with $n$ "broken lines". Gerritzen and Piwek proposed a dual perspective, a compact moduli space parametrizing certain reducible degenerations of $\mathbb{P}^2$ with $n$ smooth points. We investigate the relation between these approaches, answering a question of Kapranov from 2003.
