$E_6$-local systems from cubic threefolds

TL;DR

The paper constructs numerous local systems with $E_6$ monodromy on the moduli space of cubic threefolds, derived from the middle cohomology of abelian covers of the Fano scheme.

Contribution

It introduces a method to produce infinitely many local systems with exceptional $E_6$ monodromy from cubic threefolds.

Findings

Local systems with $E_6$ monodromy are constructed on moduli spaces.

These local systems come from the middle cohomology of abelian covers.

The construction yields infinitely many such local systems.

Abstract

We produce infinitely many local systems on (level covers of) the moduli space of smooth cubic threefolds, with algebraic monodromy group equal to the exceptional group $E_6$. These local systems arise in the middle cohomology of abelian \'etale covers of the Fano scheme parametrizing lines in the universal cubic threefold.