The notion of divisor plays an important role in the study of intrinsic geometry on a variety or a scheme. Also, the divisor class group and Picard group are interesting invariants but in general hard to calculate. However, this is not the case under the setting of toric varieties.

In this talk, after briefly recalling some basic notions, we have three main points: first, characterizing both the Weil and Cartier divisor class group of toric variety of a fan; second, comparing them under some more condition on the variety; finally, developing basic results of support functions and Cartier divisor group. If time permitting, we’ll see some examples and focus on global sections of the sheaves defined by torus invariant divisors.

Reference

Cox, Little, Schenck, Toric Varieties