Weil Classes and Decomposable Abelian Fourfolds

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• Main Author: van Geemen, Bert
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211807
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Weil Classes and Decomposable Abelian Fourfolds. Bert van Geemen. SIGMA 18 (2022), 097, 18 pages

We determine which codimension two Hodge classes on 𝐽 × 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...