Extensions and applications of the theory of toric varieties

点击翻译按钮获取中文摘要

We have studied on the extensions and applications of the theory of toric varieties. We got new results on the extensions of the concepts of fans and semigroup rings and associated toric varieties and their extensions, locally finite scheme associated to a decomposition of a real space by not necessarily bounded polytopes. We also got results on the Minkowskii sums of convex polytopes and very ampleness and normality of line bundles, normal varieties factoring Frobenius morphisms, and resolutions of higherdimensional cyclic quotient singularities.