Algebraicity of Hodge classes on some Generalized Prym Varieties

TL;DR

This paper demonstrates that specific Hodge classes on certain generalized Prym varieties are algebraic, using geometric class field theory to connect algebraic cycles with Prym constructions.

Contribution

It provides a new proof of algebraicity of Hodge classes on generalized Prym varieties via geometric class field theory, revisiting and extending Schoen's algebraic cycles.

Findings

Hodge classes on some Prym varieties are algebraic.

Construction of algebraic cycles from geometric class field theory.

Extension of Schoen's work on Prym varieties.

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.