The locus of real multiplication and the Schottky locus

TL;DR

This paper demonstrates that most points in a specific high-dimensional modular space are not Jacobians, using degeneration methods independent of previous approaches involving the mapping class group.

Contribution

It provides a new proof that the generic point of a Hilbert modular four-fold is not a Jacobian, employing degeneration techniques distinct from earlier methods.

Findings

Most points in the Hilbert modular four-fold are not Jacobians.

The proof is independent of the properties of the mapping class group.

Degeneration techniques are effective in studying the Schottky locus.

Abstract

We prove that the generic point of a Hilbert modular four-fold is not a Jacobian. The proof uses degeneration techniques and is independent of properties of the mapping class group used in preceding papers on locally symmetric subvarieties of the moduli space of abelian varieties contained in the Schottky locus.