基于Gale对偶的数值放大准则
A numerical ampleness criterion via Gale duality
摘要：
本文的主要目的是一个数值准则，确定当一个$\Q$ -阶乘完全复曲面簇的Weil因子允许一个正的多重Cartier因子，这是数值有效的（nef）或充分的。这是$\Z$的一个结果--盖尔对偶性的线性解释和我们在以前的几篇论文中发展的自洽性。作为一个副产品，我们得到了一个Weil因子的Cartier指数的计算和弱$\Q$ -Fano，$\Q$ -Fano，Gorenstein，弱Fano和Fano环面品种的数值特征。几个例子，然后给出和研究。\keywords { $\Q$ --阶乘完全复曲面品种\and样本除数\and nef除数\and $\Z$ --线性盖尔对偶\and次级风扇\and样本标准\and卡地亚指数\and $\Q$ --Fano复曲面品种。
英文摘要：
The main object of the present paper is a numerical criterion determining when a Weil divisor of a $\Q$--factorial complete toric variety admits a positive multiple Cartier divisor which is either numerically effective (nef) or ample. It is a consequence of $\Z$--linear interpretation of Gale duality and se\-con\-dary fan as developed in several previous papers of us. As a byproduct we get a computation of the Cartier index of a Weil divisor and a numerical characterization of weak $\Q$--Fano, $\Q$--Fano, Gorenstein, weak Fano and Fano toric varieties. Several examples are then given and studied. \keywords{$\Q$--factorial complete toric variety \and ample divisor \and nef divisor \and $\Z$-liner Gale duality \and secondary fan \and ampleness criterion \and Cartier index \and $\Q$-Fano toric variety.
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