论文标题
部分旗品品种和匹配场多型的组合突变的曲折变性
Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes
论文作者
论文摘要
我们研究了由Gröbner变性或部分国旗品种的热带化引起的复曲面变性。我们生产了一个新的部分旗帜变种的曲折变性，其组合由匹配的磁场和多面体的组合突变控制。我们提供了与匹配的磁场多型相关的与所得福利品种相关的多面体的明确描述。这些多面体编码了格拉斯曼尼亚人的plücker形式的单次变性的组合数据。我们将标志品种的匹配字段多台面描述为Minkowski总和，并表明所有这些多面体都是正常的。我们获得的多面有是牛顿 - 科恩科夫（Newton-Okounkov）机构的示例，用于特定的国旗品种全等级估值。此外，我们研究了一定明确定义的大型匹配场多型家族，并证明该家族中的所有多型都通过组合突变连接。最后，我们将方法应用于明确计算小司羊群和旗品品种的复曲面变性，并获得新的复杂性归化家族。
We study toric degenerations arising from Gröbner degenerations or the tropicalization of partial flag varieties. We produce a new family of toric degenerations of partial flag varieties whose combinatorics are governed by matching fields and combinatorial mutations of polytopes. We provide an explicit description of the polytopes associated with the resulting toric varieties in terms of matching field polytopes. These polytopes encode the combinatorial data of monomial degenerations of Plücker forms for the Grassmannians. We give a description of matching field polytopes of flag varieties as Minkowski sums and show that all such polytopes are normal. The polytopes we obtain are examples of Newton-Okounkov bodies for particular full-rank valuations for flag varieties. Furthermore, we study a certain explicitly-defined large family of matching field polytopes and prove that all polytopes in this family are connected by combinatorial mutations. Finally, we apply our methods to explicitly compute toric degenerations of small Grassmannians and flag varieties and obtain new families of toric degenerations.
