Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primer for the algebraic geometry of sandpiles   The Abelian Sandpile Model (ASM) is a game played on a graph realizing the
dynamics implicit in the discrete Laplacian matrix of the graph. The purpose of
this primer is to apply the theory of lattice ideals from algebraic geometry to
the Laplacian matrix, drawing out connections with the ASM. An extended summary
of the ASM and of the required algebraic geometry is provided. New results
include a characterization of graphs whose Laplacian lattice ideals are
complete intersection ideals; a new construction of arithmetically Gorenstein
ideals; a generalization to directed multigraphs of a duality theorem between
elements of the sandpile group of a graph and the graph's superstable
configurations (parking functions); and a characterization of the top Betti
number of the minimal free resolution of the Laplacian lattice ideal as the
number of elements of the sandpile group of least degree. A characterization of
all the Betti numbers is conjectured.

22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin