Extensions and applications of the theory of toric varieties

研究了复曲面簇理论的推广和应用。我们得到了关于扇和半群环概念的扩展以及相关的复曲面簇及其扩展、与不一定有界多胞形的真实的空间分解相关的局部有限方案的新结果。我们还得到了凸多面体的Minkowskii和，线丛的非常满性和正规性，Frobenius态射的正规簇分解，以及高维循环商奇点的分解。

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.