Infinitely many local systems with monodromy group E6 are constructed on moduli spaces of cubic threefolds via cohomology of abelian covers of their Fano schemes of lines.
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$E_6$-local systems from cubic threefolds
Infinitely many local systems with monodromy group E6 are constructed on moduli spaces of cubic threefolds via cohomology of abelian covers of their Fano schemes of lines.