Multiplicities of graded families of linear series and ideals
arXiv:1301.5613
Abstract
We give simple necessary and sufficient conditions on projective schemes over a field k for asymptotic limits of the growth of all graded linear series of a fixed Kodaira-Iitaka dimension to exist. We also give necessary and sufficient conditions on a local ring R of dimension d for the limit \lim_{i\rightarrow\infty}\frac{\ell_R(R/I_n)}{n^d} to exist whenever \{I_n\} is a graded family of m_R-primary ideals. We give a number of applications.
33 pages. In this version, the applications to epsilon type multiplicities in the final section are extended to hold on arbitrary unramified local rings