Smooth Fano Polytopes Arising from Finite Directed Graphs
نویسنده
چکیده
In this paper, we consider terminal reflexive polytopes arising from finite directed graphs and study the problem of deciding which directed graphs yield smooth Fano polytopes. We show that any centrally symmetric or pseudosymmetric smooth Fano polytopes can be obtained from directed graphs. Moreover, by using directed graphs, we provide new examples of smooth Fano polytopes whose corresponding varieties admit Kähler–Einstein metrics.
منابع مشابه
Toric Fano Varieties Associated to Building Sets
We characterize building sets whose associated nonsingular projective toric varieties are Fano. Furthermore, we show that all such toric Fano varieties are obtained from smooth Fano polytopes associated to finite directed graphs.
متن کاملSmooth Fano Polytopes Arising from Finite Partially Ordered Sets
Gorenstein Fano polytopes arising from finite partially ordered sets will be introduced. Then we study the problem which partially ordered sets yield smooth Fano polytopes. Introduction An integral (or lattice) polytope is a convex polytope all of whose vertices have integer coordinates. Let P ⊂ R be an integral convex polytope of dimension d. • We say that P is a Fano polytope if the origin of...
متن کاملGorenstein Fano Polytopes Arising from Order Polytopes and Chain Polytopes
Richard Stanley introduced the order polytope O(P ) and the chain polytope C(P ) arising from a finite partially ordered set P , and showed that the Ehrhart polynomial of O(P ) is equal to that of C(P ). In addition, the unimodular equivalence problem of O(P ) and C(P ) was studied by the first author and Nan Li. In the present paper, three integral convex polytopes Γ(O(P ),−O(Q)), Γ(O(P ),−C(Q...
متن کاملA Bound for the Splitting of Smooth Fano Polytopes with Many Vertices
The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such that the vertex set of each facet forms a lattice basis. Casagrande showed that any smooth d-dimensional Fano polytope has at most 3d vertices. Smooth Fano ...
متن کاملOn a Classification of Smooth Fano Polytopes
The d-dimensional simplicial, terminal, and reflexive polytopes with at least 3d − 2 vertices are classified. In particular, it turns out that all of them are smooth Fano polytopes. This improves previous results of Casagrande (2006) and Øbro (2008). Smooth Fano polytopes play a role in algebraic geometry and mathematical physics. This text is an extended abstract of Assarf et al. (2012). Résum...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014