论文标题
平面中六行的模量空间的稳定对压实的交点理论
Intersection theory of the stable pair compactification of the moduli space of six lines in the plane
论文作者
论文摘要
我们描述了$ \ Overline {M} _ {0,5} \ times \ Overline {M} _ {0,5} $和$ \ Mathbf {P}^2 \ times \ times \ times \ Mathbf {p}^2 $稳定稳定的$ \ + edrline（M Mathbf {p} 3， $ m（3,6）$的六行，$ \ mathbf {p}^2 $。这些爆炸序列可以分别视为Keel's和Kapranov的构建$ \ OVERLINE {M} _ {0，N} $的概括。我们使用这些爆炸序列来描述$ \ overline {m}（3,6）$的相交理论。特别是，我们表明，$ \ $ \叠加{m}（3,6）$的任何小分辨率的食物环具有类似于Keel的呈现的$ a^*（\ overline {m} _ {0，n}）$的介绍，而$ \ edline {m}（3,6）$ smim smim cons的Chow Ring Ring and Chow Ring Ring cons的chow ring con是chow的一部分。我们还介绍了$ \ overline {m} _ {0，n} $的$ψ$类别的高维版本，并在$ \ overline {m}（3,6）$上描述它们的相交。最后，我们使用结果来获得卢克斯顿结果的独立证明，即$ \叠加{m}（3,6）$是$ m（3,6）$的日志规范压实。
We describe sequences of blowups of $\overline{M}_{0,5} \times \overline{M}_{0,5}$ and $\mathbf{P}^2 \times \mathbf{P}^2$ yielding a small resolution of the stable pair compactification $\overline{M}(3,6)$ of the moduli space $M(3,6)$ of six lines in $\mathbf{P}^2$. These blowup sequences can be viewed, respectively, as generalizations of Keel's and Kapranov's constructions of $\overline{M}_{0,n}$. We use these blowup sequences to describe the intersection theory of $\overline{M}(3,6)$. In particular, we show that the Chow ring of any small resolution of $\overline{M}(3,6)$ has a presentation analogous to Keel's presentation of $A^*(\overline{M}_{0,n})$, and the Chow ring of $\overline{M}(3,6)$ is an explicit subring of the Chow ring of one of these small resolutions. We also introduce higher-dimensional versions of the $ψ$-classes on $\overline{M}_{0,n}$, and describe their intersections on $\overline{M}(3,6)$. Finally, we use our results to obtain an independent proof of Luxton's result that $\overline{M}(3,6)$ is the log canonical compactification of $M(3,6)$.
