Kuga Varieties of Polarised Abelian Surfaces

TL;DR

This paper investigates the Kodaira dimension of Kuga varieties linked to moduli spaces of polarized abelian surfaces with level structure, providing insights into their geometric properties for prime levels.

Contribution

It introduces a detailed study of the Kodaira dimension of Kuga varieties associated with (1,p)-polarized abelian surfaces, expanding understanding of their geometric classification.

Findings

Determined the Kodaira dimension for specific prime levels p.

Established new connections between moduli spaces and Kuga varieties.

Contributed to the classification of algebraic varieties related to abelian surfaces.

Abstract

We study the Kodaira dimension of Kuga varieties $\mathcal{X}^n_p$ associated to the moduli spaces $\mathcal{A}_p$ of $(1, p)$-polarised abelian surfaces with level structure for prime $p \geq 3$.