Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicities of graded families of linear series and ideals   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.

15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom