E₆-local systems from cubic threefolds

2026/04/22 by Thomas Krämer, Daniel Litt, Marco Maculan · 1 voice
Mathematics · #math.AG

paper · pdf

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 E₆. These local systems arise in the middle cohomology of abelian étale covers of the Fano scheme parametrizing lines in the universal cubic threefold.

Citations

• Big monodromy for higher Prym representations
• The monodromy of families of subvarieties on abelian varieties
• The Shafarevich conjecture for hypersurfaces in abelian varieties
• Compatible systems of Galois representations associated to the exceptional group E6
• Logarithmic Riemann-Hilbert correspondences for rigid varieties
• Deformations of Galois representations and exceptional monodromy, II:\n raising the level
• Characteristic cycles and the microlocal geometry of the Gauss map, I
• Remarks On the Topology of the Fano surface
• Motives with exceptional Galois groups and the inverse Galois problem

Discussions

• But so far we haven't be able to find analogous constructions for E_7 or E_8. Can you? Incidentally, you can read the paper here: arxiv.org/abs/2604.20970 16/n, n=16. [bsky, 4 points, 0 comments]

Related

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• Rigid local systems with monodromy group the Conway group Co₂
• Automorphism and Cohomology I: Fano variety of lines and Cubic