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Classification of Bagnera–de Franchis Varieties in Small Dimensions
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 111-133.

Une variété de Bagnera–de Franchis X est un quotient A/G d’une variété abélienne A par un groupe cyclique fini G=gBihol(A) agissant librement et ne consistant pas uniquement en des translations. Par une construction explicite des polarisations, et en suivant une méthode introduite par F. Catanese, nous donnons une classification exhaustive à conjugaison complexe près et au sens suivant des variétés de Bagnera–de Franchis scindées jusqu’en dimension 4 : A admet une décomposition en somme directe de sous-variétés abéliennes G-invariantes indexées par k|#G sur lesquelles la partie linéaire de g agit avec des valeurs propres d’ordre k.

A Bagnera–de Franchis variety X=A/G is the quotient of an Abelian variety A by a free action of a finite cyclic group G=gBihol(A), which does not contain only translations. Constructing explicit polarizations and using a method introduced by F. Catanese, we classify split Bagnera–de Franchis varieties (i.e., there is a direct sum decomposition of A into G-invariant Abelian subvarieties, indexed by k|#G, on which the linear part of g acts with eigenvalues of order k) up to complex conjugation in dimensions 4.

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DOI : https://doi.org/10.5802/afst.1626
@article{AFST_2020_6_29_1_111_0,
     author = {Andreas Demleitner},
     title = {Classification of Bagnera{\textendash}de Franchis Varieties in Small Dimensions},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {111--133},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 29},
     number = {1},
     year = {2020},
     doi = {10.5802/afst.1626},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1626/}
}
Andreas Demleitner. Classification of Bagnera–de Franchis Varieties in Small Dimensions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 111-133. doi : 10.5802/afst.1626. https://afst.centre-mersenne.org/articles/10.5802/afst.1626/

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