论文标题
牛顿 - 科恩科夫国旗品种和组合突变的机构
Newton-Okounkov bodies of flag varieties and combinatorial mutations
论文作者
论文摘要
牛顿 - 科恩科夫（Newton-Okounkov）机构是一个凸体，该凸体是由具有全球生成的线条捆绑包的投影品种构建的，并且在功能字段上具有较高的等级估值，这提供了一种系统的方法来构建投影品品种的复合变性。它的组合特性在很大程度上取决于估值的选择，这是将牛顿 - 科恩科夫的身体与不同类型的估值相关的基本问题。在本文中，我们使用组合突变的框架来解决标志品种的问题，该框架是在Fano歧管的镜像对称性中引入的。通过应用迭代的组合突变，我们将特定的牛顿 - 科恩科夫体系连接起来，包括字符串多型，Nakashima-Zelevinsky polytopes和FFLV多型物体。
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 FFLV polytopes.
