Abstract
Given an ample line bundle L on a geometrically reduced projective scheme defined over an arbitrary non-Archimedean field, we establish a differentiability property for the relative volume of two continuous metrics on the Berkovich analytification of L, extending previously known results in the discretely valued case. As applications, we provide fundamental solutions to certain non-Archimedean ...
Abstract
Given an ample line bundle L on a geometrically reduced projective scheme defined over an arbitrary non-Archimedean field, we establish a differentiability property for the relative volume of two continuous metrics on the Berkovich analytification of L, extending previously known results in the discretely valued case. As applications, we provide fundamental solutions to certain non-Archimedean Monge-Ampere equations and generalize an equidistribution result for Fekete points. Our main technical input comes from determinant of cohomology and Deligne pairings.
Altmetric