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Fiber cones and analytic spreads of the canonical and anticanonical ideals and limit Frobenius complexity of Hibi rings. (arXiv:1804.01046v2 [math.AC] UPDATED)
来源于:arXiv
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 P 查看全文>>