2011/12/14 by Éveline Legendre, Legendre, Eveline · 1 citation
Mathematics · #32Q20 (Primary) 53C99 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1112.3239
openalex publication_date 2011/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that any compact convex simple lattice polytope is the moment polytope of a Kähler-Einstein orbifold, unique up to orbifold covering and homothety. We extend the Wang-Zhu Theorem \citeWZ giving the existence of a Kähler-Ricci soliton on any toric monotone manifold on any compact convex simple labelled polytope satisfying the combinatoric condition corresponding to monotonicity. We obtain that any compact convex simple polytope P⊂ \bRn admits a set of inward normals, unique up to dilatation, such that there exists a symplectic potential satisfying the Guillemin boundary condition (with respect to these normals) and the Kähler-Einstein equation on P× \bRn. We interpret our result in terms of existence of singular Kähler-Einstein metrics on toric manifolds.