$E_6$-local systems from cubic threefolds

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 étale covers of the Fano scheme parametrizing lines in the universal cubic threefold.

26 pages, 1 figure, comments welcome