标题： KSBA 与模空间的$D_{1,6}$-极化 Enriques 曲面的紧化 显示英文标题

标题： The KSBA compactification of the moduli space of $D_{1,6}$-polarized Enriques surfaces

摘要： 我们描述了由稳定对（也称为KSBA紧化）的Enriques曲面的$4$维族，这些曲面是$\mathbb{Z}_2^2$覆盖了$\mathbb{P}^2$在三个一般点处的爆破，并沿着三对线的配置分支。 在有限群作用下，我们证明该紧化与单位立方体的次多面体相关的环面簇同构。 我们将所考虑的KSBA紧化与同一Enriques曲面族的Baily-Borel紧化相关联。 KSBA边界的一部分具有环面行为，另一部分与Baily-Borel紧化同构，剩下的部分则是这两者的混合。 我们将此处研究的稳定对紧化与Looijenga的半环面紧化相关联。 显示英文摘要

摘要： We describe a compactification by stable pairs (also known as KSBA compactification) of the $4$-dimensional family of Enriques surfaces which arise as the $\mathbb{Z}_2^2$-covers of the blow up of $\mathbb{P}^2$ at three general points branched along a configuration of three pairs of lines. Up to a finite group action, we show that this compactification is isomorphic to the toric variety associated to the secondary polytope of the unit cube. We relate the KSBA compactification considered to the Baily-Borel compactification of the same family of Enriques surfaces. Part of the KSBA boundary has a toroidal behavior, another part is isomorphic to the Baily-Borel compactification, and what remains is a mixture of these two. We relate the stable pair compactification studied here with Looijenga's semitoric compactifications.