论文标题
曲曲面的规范模型
Canonical models of toric hypersurfaces
论文作者
论文摘要
令$ z $为$ d $ d $ d $ d $ demensional torus $（\ mathbb {c}^*）^d $由laurent polyenmial $ f $带有$ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d，子集$ f（p）\子集p $由$ p $中的所有积分组成，具有积分距离至少$ 1 $的所有积分支撑$ p $的整体支架称为$ p $的罚款内部。如果$ f（p）\ neq \ emptySet $，我们构建了$ z $的独特投影模型$ \ widetilde {z} $在最坏的规范奇异点处，并获得最小的模型$ \ hat $ \ hat $ \ hat $ z} $ z $ of crepant morphisms $ \ hat {z} \ to {z} \ to {z} \ to \ to \ wideTeLde = z}我们表明，kodaira尺寸$κ=κ（\ widetilde {z}）$等于$ \ min \ {d-1，\ dim f（p）\} $和一般的iitaka纤维在规范的模型$ \ wideTilde $ \ wideTilde {z} $ tor {z} $的$ \ \ \ dimenter的$（dimenter）$（dimenter）$（d-1- dementer）$（d-1）。 kodaira dimension $ 0 $。使用$ f（p）$，我们获得了一个简单的组合公式，用于交叉数字$（k _ {\ widetilde {z}}}）^{d-1} $。
Let $Z$ be a nondegenerate hypersurface in $d$-dimensional torus $(\mathbb{C}^*)^d$ defined by a Laurent polynomial $f$ with a $d$-dimensional Newton polytope $P$. The subset $F(P) \subset P$ consisting of all points in $P$ having integral distance at least $1$ to all integral supporting hyperplanes of $P$ is called the Fine interior of $P$. If $F(P) \neq \emptyset$ we construct a unique projective model $\widetilde{Z}$ of $Z$ having at worst canonical singularities and obtain minimal models $\hat{Z}$ of $Z$ by crepant morphisms $\hat{Z}\to \widetilde{Z}$. We show that the Kodaira dimension $κ=κ(\widetilde{Z})$ equals $\min \{ d-1, \dim F(P) \}$ and the general fibers in the Iitaka fibration of the canonical model $\widetilde{Z}$ are non\-degenerate $(d-1-κ)$-dimensional toric hypersurfaces of Kodaira dimension $0$. Using $F(P)$, we obtain a simple combinatorial formula for the intersection number $(K_{\widetilde{Z}})^{d-1}$.
