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arXiv · 2407.17260

A strong counterexample to the log canonical Beauville--Bogomolov decomposition

Fabio Bernasconi·Stefano Filipazzi·Zsolt Patakfalvi·Nikolaos Tsakanikas
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Abstract

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.

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Fabio Bernasconi, Stefano Filipazzi, Zsolt Patakfalvi, Nikolaos Tsakanikas. 2026-05-07. A strong counterexample to the log canonical Beauville--Bogomolov decomposition. https://arxiv.org/abs/2407.17260

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