Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Ideal Generation Problem for Fat Points   This paper is concerned with determining the number of generators in each
degree for minimal sets of homogeneous generators for saturated ideals defining
fat point subschemes $Z=m_1p_1+ ... +m_rp_r$ for general sets of points $p_i$
of $P^2$. For thin points (i.e., m_i=1 for all i), a solution is known, in
terms of a maximal rank property. Although this property in general fails for
fat points, we show it holds in an appropriate asymptotic sense. In the uniform
(i.e., $m_1= ... =m_r$) case, we determine all failures of this maximal rank
property for $r\le 9$, and we develop evidence for the conjecture that no other
failures occur for $r > 9$.

16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th