论文标题
组合突变和块对角线
Combinatorial Mutations and Block Diagonal Polytopes
论文作者
论文摘要
Sturmfels和Zelevinsky引入了匹配场，以研究某些牛顿多面有，最近已显示出来引起各种品种家族的复曲面变性。每当匹配场产生曲折的变性时，感谢您的多体都与匹配的磁场多型重合。我们研究了组合突变，它们是匹配田间多面体的聚类突变的类似物，并表明通过突变保留了产生草个植物的曲折性变性的特性。此外，通过突变产生的多面体是牛顿 - 科恩科夫（Newton-Okounkov）在某些全级估值方面为拉格曼人提供的。我们生产了一大批这样的多面体，扩大了所谓的块对角匹配场的家庭。
Matching fields were introduced by Sturmfels and Zelevinsky to study certain Newton polytopes and more recently have been shown to give rise to toric degenerations of various families of varieties. Whenever a matching field gives rise to a toric degeneration, the associated polytope of the toric variety coincides with the matching field polytope. We study combinatorial mutations, which are analogues of cluster mutations for polytopes, of matching field polytopes and show that the property of giving rise to a toric degeneration of the Grassmannians, is preserved by mutation. Moreover the polytopes arising through mutations are Newton-Okounkov bodies for the Grassmannians with respect to certain full-rank valuations. We produce a large family of such polytopes, extending the family of so-called block diagonal matching fields.
