Georgia Institute of Technology College of Sciences

How does one study the asymptotic properties for the Hilbert series of a module? In this talk, we will examine the function which sends the numerator of the rational function representing the Hilbert series of a module to that of its r-th Veronese submodule. As r tends to infinity, the behaviour of this function depends only on the multidegree of the module and the underlying multigraded polynomial ring. More importantly, we will give a polyhedral description for the asymptotic polynomial and show that the coefficients are log-concave.