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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.21889 |
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Table of Contents:
- For a smooth projective complex variety $X$, we prove that there exists a birational morphism $X\times X\to Y$ to a projective variety $Y$ contracting the diagonal $Δ_X\subset X\times X$ to a point if and only if $X$ has maximal Albanese dimension and irregularity $q\geq 2\dim X$. We also give necessary and sufficient conditions for arbitrary contractions of the diagonal and for the existence of a birational morphism which is an isomorphism outside the diagonal.