Minimal multiplicity of fiber components in abelian fibrations
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 m1, ..., mk be the multiplicities of its irreducible components. We prove that the minimum of mi is equal to their greatest common divisor gcd(m1, ..., mk)
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