Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fiber cones, analytic spreads of the canonical and anticanonical ideals
  and limit Frobenius complexity of Hibi rings   Let ${\cal R}_{\mathbb{K}}[H]$ be the Hibi ring over a field $\mathbb{K}$ on
a finite distributive lattice $H$, $P$ the set of join-irreducible elements of
$H$ and $\omega$ the canonical ideal of ${\cal R}_{\mathbb{K}}[H]$. We show the
powers $\omega^{(n)}$ of $\omega$ in the group of divisors $\mathrm{Div}({\cal
R}_{\mathbb{K}}[H])$ is identical with the ordinal powers of $\omega$, describe
the $\mathbb{K}$-vector space basis of $\omega^{(n)}$ for $n\in\mathbb{Z}$.
Further, we show that the fiber cones $\bigoplus_{n\geq
0}\omega^n/\mathfrak{m}\omega^n$ and
$\bigoplus_{n\geq0}(\omega^{(-1)})^n/\mathfrak{m}(\omega^{(-1)})^n$ of $\omega$
and $\omega^{(-1)}$ are sum of the Ehrhart rings, defined by sequences of
elements of $P$ with a certain condition, which are polytopal complex version
of Stanley-Reisner rings. Moreover, we show that the analytic spread of
$\omega$ and $\omega^{(-1)}$ are maximum of the dimensions of these Ehrhart
rings. Using these facts, we show that the question of Page about Frobenius
complexity is affirmative: $\lim_{p\to\infty}\mathrm{cx}_F({\cal
R}_{\mathbb{K}}[H])=
\dim(\bigoplus_{n\geq0}\omega^{(-n)}/\mathfrak{m}\omega^{(-n)})-1$, where $p$
is the characteristic of the field $\mathbb{K}$.

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The categories of this paper are: cs
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga