Minimal multiplicity of fiber components in abelian fibrations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866911340414631936 |
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| author | Campana, Frederic Kamenova, Ljudmila Verbitsky, Misha |
| author_facet | Campana, Frederic Kamenova, Ljudmila Verbitsky, Misha |
| contents | 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 $gcd(m_1, ..., m_k)$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal multiplicity of fiber components in abelian fibrations Campana, Frederic Kamenova, Ljudmila Verbitsky, Misha Algebraic Geometry 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 $gcd(m_1, ..., m_k)$ |
| title | Minimal multiplicity of fiber components in abelian fibrations |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.14607 |