Geodesic
Weil Classes and Decomposable Abelian Fourfolds
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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We determine which codimension two Hodge classes on $J\times J$, where $J$ is a general abelian surface, deform to Hodge classes on a family of abelian fourfolds of Weil type. If a Hodge class deforms, there is in general a unique such family. We show how to determine the imaginary quadratic field acting on the fourfolds of Weil type in this family as well as their polarization. There are Hodge classes that may deform to more than one family. We relate these to Markman's Cayley classes.
Keywords: abelian varieties, Hodge classes. 
@article{SIGMA_2022_18_a96,
     author = {Bert van Geemen},
     title = {Weil {Classes} and {Decomposable} {Abelian} {Fourfolds}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a96/}
}
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Bert van Geemen. Weil Classes and Decomposable Abelian Fourfolds. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a96/

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