A strong counterexample to the log canonical Beauville--Bogomolov decomposition
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909023768412160 |
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| author | Bernasconi, Fabio Filipazzi, Stefano Patakfalvi, Zsolt Tsakanikas, Nikolaos |
| author_facet | Bernasconi, Fabio Filipazzi, Stefano Patakfalvi, Zsolt Tsakanikas, Nikolaos |
| contents | For every $d \geq 4$, we construct a $d$-dimensional, log canonical, $K$-trivial variety with the property that two general fibers of its Albanese morphism are not birational. This provides a strong counterexample to the Beauville--Bogomolov decomposition in the log canonical setting. This construction can also be adapted to construct a smooth quasi-projective variety of logarithmic Kodaira dimension 0 whose quasi-Albanese morphism has maximal variation. On the positive side, we show that the Albanese morphism for log canonical pairs with nef anti-canonical class is a locally stable family of pairs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_17260 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A strong counterexample to the log canonical Beauville--Bogomolov decomposition Bernasconi, Fabio Filipazzi, Stefano Patakfalvi, Zsolt Tsakanikas, Nikolaos Algebraic Geometry Differential Geometry For every $d \geq 4$, we construct a $d$-dimensional, log canonical, $K$-trivial variety with the property that two general fibers of its Albanese morphism are not birational. This provides a strong counterexample to the Beauville--Bogomolov decomposition in the log canonical setting. This construction can also be adapted to construct a smooth quasi-projective variety of logarithmic Kodaira dimension 0 whose quasi-Albanese morphism has maximal variation. On the positive side, we show that the Albanese morphism for log canonical pairs with nef anti-canonical class is a locally stable family of pairs. |
| title | A strong counterexample to the log canonical Beauville--Bogomolov decomposition |
| topic | Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2407.17260 |