Weil Classes and Decomposable Abelian Fourfolds

DOI10.3842/SIGMA.2022.097arXiv2108.02087MaRDI QIDQ6374505

Bert Van Geemen

Publication date: 4 August 2021

Abstract: We determine which codimension two Hodge classes on $JimesJ$, 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.

Mathematics Subject Classification ID

Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Algebraic cycles (14C25) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

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