紧致光滑环簇上的解析向量场

Analytic vector fields on compact smooth toric varieties

本文通过多面体来刻画紧致光滑环簇上解析向量场所构成的向量空间的维数.首先,通过对一些具体的光滑环簇上解析向量场的研究,作者对解析向量场结构有了一个直观认识,并且发现它们与多面体之间存在某种关系;进而作者发现对一般的紧致光滑环簇,解析向量场向量空间的维数等于其对应多面体商集中整点的个数.

This paper studies the dimension of the vector space of analytic vector fields on a compact smooth toric variety. Firstly, by the study of some examples, the authors obtain a visual literacy for the construction of the analytic vector fields and discover some relations between them and polytopes; and then, they come to study general compact smooth toric varieties, and find that the dimension of the vector space of analytic vector fields on a compact smooth toric variety is equal to the number of integral point in the quotient set of polotopes.