OKOUNKOV BODIES: AN APPROACH OF FUNCTION FIELD ARITHMETIC

Overview & Synopsis

By using the method of function field arithmetic, we associate, to each graded linear series which is birational and of sub-finite type, a convex body whose Lebesgue measure identifies with the volume of the graded linear series. This approach allows to remove the hypothesis on the existence of a regular rational point, which appears for example in the construction of Lazarsfeld and Mustata Moreover, it requires less non-intrinsic parameters of the projective variety.