Minimal multiplicity of fiber components in abelian fibrations

Frederic Campana; Ljudmila Kamenova; Misha Verbitsky

paper

Minimal multiplicity of fiber components in abelian fibrations

arXiv:2512.14607

Abstract

An abelian fibration is a proper projective surjective map of complex varieties with general fiber an abelian variety. Consider a multiple fiber of an abelian fibration, and let $m_{1}, ..., m_{k}$ be the multiplicities of its irreducible components. We prove that the minimum of $m_{i}$ is equal to their greatest common divisor $g c d (m_{1}, ..., m_{k})$

9 pages, v. 2.1, added more reference, corrected an error