Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic $h$-vectors of simplicial complexes through local cohomology,
  part 1   Given an infinite field $\mathbb{k}$ and a simplicial complex $\Delta$, a
common theme in studying the $f$- and $h$-vectors of $\Delta$ has been the
consideration of the Hilbert series of the Stanley--Reisner ring
$\mathbb{k}[\Delta]$ modulo a generic linear system of parameters $\Theta$.
Historically, these computations have been restricted to special classes of
complexes (most typically triangulations of spheres or manifolds). We provide a
compact topological expression of $h_{d-1}^\mathfrak{a}(\Delta)$, the dimension
over $\mathbb{k}$ in degree $d-1$ of $\mathbb{k}[\Delta]/(\Theta)$, for any
complex $\Delta$ of dimension $d-1$. In the process, we provide tools and
techniques for the possible extension to other coefficients in the Hilbert
series.

12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph