Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry, Unimodality, and Lefschetz Properties for Graded Modules   If $\mbk$ is algebraically closed of characteristic zero and $R = \mbk[x,y,
z]$, we first investigate the Weak Lefschetz Property for the finite length
$R$-module $M$ that is the cokernel of a map $\vp: \bds_{j=1}^{n+2}
R(-b_j)\to\bds_{i=1}^n R(-a_i)$. Before doing so, we spend significant time
discuss the minimal free resolution of $M$, which we use to prove useful
results on the symmetry and unimodality of the Hilbert function of $M$. Lastly,
we define the\textit{non-Lefschetz locus} for finite length graded modules in
arbitrary codimension, as well as proving several results in this direction.
Moreover, we also discuss the connection with Artin level modules, the
non-Lefschetz locus, and Lefschetz properties for graded modules of finite
length in arbitrary codimension.

28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ