# 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

Department of Mathematics, University of Chicago, Chicago, IL 60637

Simion Filip

Department of Mathematics, Harvard University, Cambridge, MA 02138

Alex Wright

Department of Mathematics, Stanford University, Stanford, CA 94305