Minimal multiplicity of fiber components in abelian fibrations

Frederic Campana; Ljudmila Kamenova; Misha Verbitsky

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arXiv · 2512.14607

Minimal multiplicity of fiber components in abelian fibrations

Frederic Campana·Ljudmila Kamenova·Misha Verbitsky

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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 $gcd(m_1, ..., m_k)$

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Frederic Campana, Ljudmila Kamenova, Misha Verbitsky. 2025-12-16. Minimal multiplicity of fiber components in abelian fibrations. https://arxiv.org/abs/2512.14607

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