First proof of broad case of Ewald's conjecture on symmetric points in monotone lattice polytopes in arbitrary dimension, with partial results on Nill's conjecture and two new polytope classes.
Obro,An algorithm for the classification of smooth Fano polytopes.Preprint
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
We present an algorithm that produces the classification list of smooth Fano d-polytopes for any given d. The input of the algorithm is a single number, namely the positive integer d. The algorithm has been used to classify smooth Fano d-polytopes for d<=7. There are 7622 isomorphism classes of smooth Fano 6-polytopes and 72256 isomorphism classes of smooth Fano 7-polytopes.
verdicts
UNVERDICTED 2representative citing papers
Gorenstein toric contact manifolds show flexibility where multiple toric diagrams share Ehrhart polynomials matching the cross-polytope, but rigidity where the small cross-polytope is the unique diagram for its polynomial, determining the manifold from contact Betti numbers.
citing papers explorer
-
Ewald's Conjecture and integer points in algebraic and symplectic toric geometry
First proof of broad case of Ewald's conjecture on symmetric points in monotone lattice polytopes in arbitrary dimension, with partial results on Nill's conjecture and two new polytope classes.
-
Contact flexibility and rigidity for toric Gorenstein prequantizations and Ehrhart theory of toric diagrams
Gorenstein toric contact manifolds show flexibility where multiple toric diagrams share Ehrhart polynomials matching the cross-polytope, but rigidity where the small cross-polytope is the unique diagram for its polynomial, determining the manifold from contact Betti numbers.