Bloch's principle for holomorphic maps into subvarieties of semi-abelian varieties

2023/04/12 by Yamanoi, Katsutoshi
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.05715

Abstract

We generalize a fundamental theorem in higher dimensional value distribution theory about entire curves in subvarieties X of semi-abelian varieties to the situation of the sequences of holomorphic maps from the unit disc into X. This generalization implies, among other things, that subvarieties of log general type in semi-abelian varieties are pseudo-Kobayashi hyperbolic. As another application, we improve a classical theorem due to Cartan in 1920's about the system of nowhere vanishing holomorphic functions on the unit disc satisfying Borel's identity.

Related

• Meromorphic maps from \Bbb C^p into semi-abelian varieties and general projective varieties
• Non-archimedean entire curves in closed subvarieties of semi-abelian varieties
• Semi-Bloch functions in several complex variables
• An application of the value distribution theory for semi-abelian varieties to problems of Ax-Lindemann and Manin-Mumford types
• Degeneracy of Holomorphic Curves into Algebraic Varieties