Newton-Okounkov bodies of flag varieties and combinatorial mutations
Newton-Okounkov bodies of flag varieties and combinatorial mutations
复制标题
标志品种的牛顿-奥孔科夫体和组合突变
DOI：
10.1093/imrn/rnaa276
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发表时间：
2021
影响因子：
1
通讯作者：
Naoki Fujita and Akihiro Higashitani
中科院分区：
文献类型：
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作者：
Naoki Fujita and Akihiro Higashitani
牛顿-奥孔科夫体是由具有全局生成的线丛的射影簇构造的凸体，并且在函数场上具有更高的等级评估，这给出了构造射影簇的环面退化的系统方法。其组合性质在很大程度上取决于估值的选择，将牛顿-奥孔科夫体与不同类型的估值联系起来是一个基本问题。在本文中，我们使用组合突变框架解决了标志变体的这个问题，该框架是在 Fano 流形镜像对称的背景下引入的。通过应用迭代组合突变，我们连接了标志品种的特定牛顿-奥孔科夫体，包括弦多胞体、中岛-泽列文斯基多胞体和费金-傅里叶-利特曼-温伯格多胞体。
A Newton–Okounkov body is a convex body constructed from a projective variety with a globally generated line bundle and with a higher rank valuation on the function field, which gives a systematic method of constructing toric degenerations of projective varieties. Its combinatorial properties heavily depend on the choice of a valuation, and it is a fundamental problem to relate Newton–Okounkov bodies associated with different kinds of valuations. In this paper, we address this problem for flag varieties using the framework of combinatorial mutations, which was introduced in the context of mirror symmetry for Fano manifolds. By applying iterated combinatorial mutations, we connect specific Newton–Okounkov bodies of flag varieties including string polytopes, Nakashima–Zelevinsky polytopes, and Feigin–Fourier–Littelmann–Vinberg polytopes.