The algebraic hull of the Kontsevich–Zorich cocycle

Abstract

We compute the algebraic hull of the Kontsevich–Zorich cocycle over any $ \mathrm {GL}^+_2(\mathbb {R}) $ invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.

Authors

Alex Eskin

University of Chicago, Chicago, IL

Simion Filip

Harvard University, Cambridge, MA

Alex Wright

Stanford University, Stanford, CA