论文标题
循环商奇点平滑的反典型模型
Anticanonical models of smoothings of cyclic quotient singularities
论文作者
论文摘要
考虑到y $中的表面循环商$ q \ $ q \，确定$ y $的所有平滑$ y $是一个开放的问题，该$ y $容纳了抗宗教模型并进行计算。在[htu]中，hacking，tevelev和urzúa研究了$ y $的广泛变形空间中的某些不可约组件，在这些组件中，他们找到了一个参数平滑$ \ nathcal {y} \ to \ to \ to \ to \ m mathbb {a}^1 $，该^1 $允许抗药性模型，并且可以证明他们可以证明他们的歌唱。此外，他们明确计算使用MORI的除法算法具有最终奇异性的抗宪法模型[M02]。我们研究了这些组件中的一个参数平滑，该参数允许具有规范但非末端奇异性的抗宪法模型，目的是将它们完全分类。我们确定了某些类别的“对角线”平滑，其中总空间是三倍的三倍，并且我们使用感谢您的MMP明确构建了抗神日模型。
Given a surface cyclic quotient singularity $Q\in Y$, it is an open problem to determine all smoothings of $Y$ that admit an anticanonical model and to compute it. In [HTU], Hacking, Tevelev, and Urzúa studied certain irreducible components of the versal deformation space of $Y$, and within these components, they found one parameter smoothings $\mathcal{Y} \to \mathbb{A}^1$ that admit an anticanonical model and proved that they have canonical singularities. Moreover, they compute explicitly the anticanonical models that have terminal singularities using Mori's division algorithm [M02]. We study one parameter smoothings in these components that admit an anticanonical model with canonical but non-terminal singularities with the goal of classifying them completely. We identify certain class of "diagonal" smoothings where the total space is a toric threefold and we construct the anticanonical model explicitly using the toric MMP.
