Holomorphic curves in compact Shimura varieties
Emmanuel Ullmo, Andrei Yafaev
TL;DR
This paper establishes a hyperbolic analogue of the Bloch-Ochiai theorem, describing the Zariski closure of holomorphic curves within compact Shimura varieties, extending classical results in complex geometry.
Contribution
It introduces a new hyperbolic version of the Bloch-Ochiai theorem applicable to compact Shimura varieties, expanding understanding of holomorphic curves in these spaces.
Findings
Proves a hyperbolic analogue of the Bloch-Ochiai theorem.
Describes the Zariski closure of holomorphic curves in Shimura varieties.
Extends classical complex geometry results to hyperbolic contexts.
Abstract
We prove a hyperbolic analogue of the Bloch-Ochiai theorem about the Zariski closure of holomorphic curves in abelian varieties.
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Taxonomy
TopicsMeromorphic and Entire Functions · Algebraic Geometry and Number Theory · Geometry and complex manifolds