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A sufficient condition for a Hibi ring to be level and levelness of Schubert cycles

Mitsuhiro Miyazaki
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Abstract

Let $K$ be a field, $D$ a finite distributive lattice and $P$ the set of all join-irreducible elements of $D$. We show that if $\{y\in P\mid y\geq x\}$ is pure for any $x\in P$, then the Hibi ring $\RRRRR_K(D)$ is level. Using this result and the argument of sagbi basis theory, we show that the homogeneous coordinate rings of Schubert subvarieties of Grassmannians are level.

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Mitsuhiro Miyazaki. 2005-01-23. A sufficient condition for a Hibi ring to be level and levelness of Schubert cycles. https://arxiv.org/abs/math/0501390

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