Matroid theory describes conic divisorial ideals via polytopes in toric rings from root systems; for signed-poset rings R_P the divisor class group is computed and the Q-Gorenstein property is characterized in terms of P, extending Hibi-ring results.
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Toric Schubert varieties in partial flag varieties admit an explicit combinatorial fan model via Deodhar decompositions, yielding necessary and sufficient smoothness conditions in terms of Cartan integers along with supersolvable lattice structure for certain Weyl group intervals.
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Toric rings associated with root systems and conic divisorial ideals via matroid theory
Matroid theory describes conic divisorial ideals via polytopes in toric rings from root systems; for signed-poset rings R_P the divisor class group is computed and the Q-Gorenstein property is characterized in terms of P, extending Hibi-ring results.
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Toric Schubert Varieties in Partial Flag Varieties
Toric Schubert varieties in partial flag varieties admit an explicit combinatorial fan model via Deodhar decompositions, yielding necessary and sufficient smoothness conditions in terms of Cartan integers along with supersolvable lattice structure for certain Weyl group intervals.