Introduction to Okounkov bodies and some recent developments


Jow Shin-Yao

13:30:00 - 14:30:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Given a big divisor D on an n-dimensional projective variety, one can associate a convex body in the Euclidean n-space, called the Okounkov body of D, which contains rich numerical information about D. For example, the volume of the Okounkov body of D tells us the growth rate of the dimension of the linear system |mD| as m grows. In this talk, we will give an introduction to the basic theory of Okounkov bodies and sketch some recent developments.