2020/05/14 by Robert J. Berman, Berman, Robert J. · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2005.07053
openalex publication_date 2020/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that any affine toric variety Y, which is Q-Gorenstein, admits a conical Ricci flat Kahler metric, which is smooth on the regular locus of Y. The corresponding Reeb vector is the unique minimizer of the volume functional on the Reeb cone of Y. The case when the vertex point of Y is an isolated singularity was previously shown by Futaki-Ono-Wang. The proof is based on an existence result for the inhomogeneous Monge-Ampere equation in real Euclidean space with exponential right hand side and prescribed target given by a proper convex convex, combined with transversal a priori estimates on Y.