Algebraic approximations of fibrations in abelian varieties over a curve

TL;DR

This paper proves that fibrations with abelian variety fibers over a curve can be approximated algebraically, advancing understanding of their structure within complex geometry.

Contribution

It establishes that any fibration from a compact Kähler manifold to a curve with abelian variety fibers admits an algebraic approximation, a new result in algebraic geometry.

Findings

Fibrations with abelian fibers over a curve can be approximated algebraically.

The result applies to compact Kähler manifolds with such fibrations.

This advances the understanding of the algebraic structure of these fibrations.

Abstract

For every fibration $f : X \to B$ with $X$ a compact K\"ahler manifold, $B$ a smooth projective curve, and a general fiber of $f$ an abelian variety, we prove that $f$ has an algebraic approximation.