Rigid Gorenstein toric Fano varieties arising from directed graphs
Rigid Gorenstein toric Fano varieties arising from directed graphs
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由有向图产生的刚性 Gorenstein toric Fano 簇
DOI：
10.1007/s13348-022-00350-z
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发表时间：
2022
影响因子：
1.1
通讯作者：
Tsuchiya Akiyoshi
中科院分区：
文献类型：
--
作者：
Kara Selvi;Portakal Irem;Tsuchiya Akiyoshi
有向边多面体是由根系统和有限有向图G产生的格多面体。如果G的每条有向边都属于有向圈，那么它是末端的且是自反的，也就是说，人们可以把这个多面体与具有末端奇异性的Gorenstein环面Fano变体联系在一起。Totaro证明了余维2光滑、余维3-阶乘的环状Fano簇是刚性的。本文对所有在余维2上光滑，在余维3上-阶乘的有向图进行了分类。
A directed edge polytopeis a lattice polytope arising from root systemand a finite directed graphG. If every directed edge ofGbelongs to a directed cycle inG, thenis terminal and reflexive, that is, one can associate this polytope to a Gorenstein toric Fano varietywith terminal singularities. It is shown by Totaro that a toric Fano variety which is smooth in codimension 2 and-factorial in codimension 3 is rigid. In the present paper, we classify all directed graphsGsuch thatis a toric Fano variety which is smooth in codimension 2 and-factorial in codimension 3.