论文标题
Gröbner的Hibi理想，普遍的Hibi理想和国旗品种的粉丝
Gröbner fans of Hibi ideals, generalized Hibi ideals and flag varieties
论文作者
论文摘要
本文的主要目的是在Plücker理想的Gröbner粉丝中对两个最大锥的明确描述。这些锥体对应于Semistandard和Pbw-Semistandard Young Tableaux给出的单一理想。对于第一个锥体，作为中间结果，我们获得了任何Hibi理想的Gröbner粉丝中最大锥的描述。第二，我们通过将一个理想与每个插值多室相关联，从而概括了Hibi理想的概念。这是一个多面体的家族，它概括了poset的顺序和链层（àlafang-fourier-litza-pegel）。然后，我们描述了每个理想的gröbner粉丝中的最大锥体。我们还建立了一些有关PBW-SemistArdness的有用事实，我们证明它在Plücker代数上提供了新的Hodge代数结构。
The main goal of this paper is to give explicit descriptions of two maximal cones in the Gröbner fan of the Plücker ideal. These cones correspond to the monomial ideals given by semistandard and PBW-semistandard Young tableaux. For the first cone, as an intermediate result we obtain the description of a maximal cone in the Gröbner fan of any Hibi ideal. For the second, we generalize the notion of Hibi ideals by associating an ideal with every interpolating polytope. This is a family of polytopes that generalizes the order and chain polytopes of a poset (à la Fang--Fourier--Litza--Pegel). We then describe a maximal cone in the Gröbner fan of each of these ideals. We also establish some useful facts concerning PBW-semistandardness, in particular, we prove that it provides a new Hodge algebra structure on the Plücker algebra.
