Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Algorithm for Fat Points on P2   Let $F$ be a line bundle on the blow-up $X$ of $P^2$ at $r$ general points
$p_1, ..., p_r$ and let $L$ be the pullback to $X$ of the line bundle coming
from a line on $P^2$. Under reasonable hypotheses that are conjectured always
to hold if the points $p_1, ..., p_r$ are sufficiently general, it is shown
that the computation of the dimension of the cokernel of the natural map
$\mu_F:\Gamma(F)\otimes\Gamma(L)\to\Gamma(F\otimes L)$ reduces to the case that
$F$ is ample. As an application, a complete determination of the dimension of
the cokernel of $\mu_F$ is obtained when $r\le 7$, thereby solving the Ideal
Generation Problem for fat point subschemes involving up to 7 general points of
the plane and giving an algorithm depending only on the multiplicities $m_i$
for determining the modules in a minimal free resolution of the ideal defining
a fat point subscheme $m_1p_1+...+ m_7p_7$ for general points $p_i$. All
results hold for an arbitrary algebraically closed ground field $k$.

5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg