Algebraicity of Hodge classes on some Generalized Prym Varieties

2025/06/16 by Patel, Deepam, Zhang, Yilong
#14C30 #14H40 secondary #14K22 primary #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.13729

Abstract

In this article, we revisit the construction of some algebraic cycles due to Chad Schoen on certain Prym Varieties. More precisely, we show that these cycles arise naturally from (unramified) geometric class field theory, and apply it to prove the algebraicity of certain Hodge classes on some generalized Prym Varieties.

Citations

• Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds
• The Geometry and Fundamental Group of Permutation Products and Fat Diagonals
• Algebraicity of some Weil Hodge classes
• Algebraicity of some Weil Hodge Classes
• Weil classes on abelian varieties
• Jacobians and symmetric products

Related

• The Hodge Conjecture for general Prym varieties
• Quaternionic pryms and Hodge classes
• Algebraicity of some Weil Hodge classes
• Algebraicity of some Weil Hodge Classes
• Algebraic cycles on hyper-Kähler varieties of generalized Kummer type