Differentiability of relative volumes over an arbitrary non-Archimedean field

Autor:	Boucksom, Sébastien, Gubler, Walter, Martin, Florent
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory Primary 32P05 Secondary 14G22 32U15 32W20
Druh dokumentu:	Working Paper
Popis:	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--Amp\`ere equations, and generalize an equidistribution result for Fekete points. Our main technical input comes from determinant of cohomology and Deligne pairings. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.03847 Zobrazit plný text záznamu View this record from Arxiv