Kobayashi hyperbolicity of complete linear systems on abelian varieties
Federico Caucci
TL;DR
This paper establishes a geometric criterion under which most elements of a complete linear system on an abelian variety are Kobayashi hyperbolic, contributing to the understanding of complex hyperbolic geometry.
Contribution
It introduces a new geometric condition that guarantees Kobayashi hyperbolicity for general elements of linear systems on abelian varieties.
Findings
A specific geometric condition ensures hyperbolicity.
Most elements in the linear system are Kobayashi hyperbolic under this condition.
Related conjectures are proposed for further research.
Abstract
We provide a geometric condition ensuring that a very general element of a complete linear system on an abelian variety is Kobayashi hyperbolic. Some related conjectures are also given.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometry and complex manifolds · Geometric and Algebraic Topology