Hyperbolicity notions for varieties defined over a non-Archimedean field

2018/01/08 by Vázquez, Rita Rodríguez
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.02479

Abstract

Firstly, we pursue the work of W. Cherry on the analogue of the Kobayashi semi distance dCK that he introduced for analytic spaces defined over a non-Archimedean metrized field k. We prove various characterizations of smooth projective varieties for which dCK is an actual distance. Secondly, we explore several notions of hyperbolicity for a smooth algebraic curve X defined over k. We prove a non-Archimedean analogue of the equivalence between having negative Euler characteristic and the normality of certain families of analytic maps taking values in X.

Related

• Non-archimedean entire curves in closed subvarieties of semi-abelian varieties
• Non-archimedean hyperbolicity of the moduli space of curves
• Hyperbolicity of varieties supporting a variation of Hodge structure
• About the hyperbolicity of complete intersections
• Logarithmic vector fields and hyperbolicity