Asymptotic Hilbert Polynomial and limiting shapes
  The main aim of this paper is to provide a method which allows finding limiting shapes of symbolic generic initial systems of higher-dimensional subvarieties of P^n. M. Mustata and S. Mayes established a connection between volumes of complements of limiting shapes and the asymptotic multiplicity for ideals of points. In the paper we prove a generalization of this fact to higher-dimensional sets. 
Marcin Dumnicki, Justyna Szpond, Halszka Tutaj-Gasinska
math.AG math.AC