A counterexample to the log canonical Beauville--Bogomolov decomposition

Autor:	Bernasconi, Fabio, Filipazzi, Stefano, Patakfalvi, Zsolt, Tsakanikas, Nikolaos
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	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. Comment: 22 pages, comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.17260 Zobrazit plný text záznamu View this record from Arxiv