Geometry of Schreieder's varieties and some elliptic and K3 moduli curves

TL;DR

This paper explores the geometric properties of Schreieder's varieties, revealing their connections to elliptic modular surfaces and families of K3 surfaces with high Picard rank, highlighting their Hodge-theoretic significance.

Contribution

It demonstrates that Schreieder's surfaces can be viewed as elliptic modular surfaces and their threefolds as families of high Picard rank K3 surfaces, providing new geometric insights.

Findings

Schreieder's surfaces are elliptic modular surfaces.

Schreieder's threefolds form families of Picard rank 19 K3 surfaces.

The varieties exhibit noteworthy Hodge-theoretic properties.

Abstract

We study the geometry of a class of $n$-dimensional smooth projective varieties constructed by Schreieder for their noteworthy Hodge-theoretic properties. In particular, we realize Schreieder's surfaces as elliptic modular surfaces and Schreieder's threefolds as one-dimensional families of Picard rank $19$ $K3$ surfaces.