Abstract

We study the subvariety of singular sections, the discriminant, of a base point free linear system $\left|L\right|$ on a smooth toric variety X. On one hand we describe pairs (X, L) for which the discriminant is of low dimension. Precisely, we collect some bounds on this dimension and classify those pairs whose dimension differs the bound less than or equal to two. On the other hand we study the degree of the discriminant for some relevant families on polarized toric varieties, describing their minimal values and the region of the ample cone where this minimal is attained.

中文翻译：

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复曲面品种的判别器

摘要

我们研究了基点自由线性系统的奇异部分的子变异，即判别式 $\left|升\right|$在光滑的复曲面品种X 上。一方面，我们描述了判别式为低维的对 ( X , L )。准确地说，我们收集了这个维度上的一些边界，并对维度差异小于或等于 2 的那些对进行分类。另一方面，我们研究了极化复曲面品种的一些相关家族的判别度，描述了它们的最小值和达到这个最小值的宽锥区域。