When is the diagonal contractible?
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912508918366208 |
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| author | Chen, Xi Gounelas, Frank |
| author_facet | Chen, Xi Gounelas, Frank |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When is the diagonal contractible? Chen, Xi Gounelas, Frank Algebraic Geometry 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. |
| title | When is the diagonal contractible? |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2507.21889 |