The algebraic hull of the Kontsevich–Zorich cocycle

Alex Eskin; Simion Filip; Alex Wright

doi:https://doi.org/10.4007/annals.2018.188.1.5

Pages 281-313 from Volume 188 (2018), Issue 1 by Alex Eskin, Simion Filip, Alex Wright

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.

Mathematical Subject Classification

Primary 2000: 14D07, 32G15, 37C85, 7D40

Milestones

Received: 9 February 2017
Revised: 8 February 2018
Accepted: 8 March 2018
Published online: 15 June 2018

Authors

Alex Eskin

University of Chicago, Chicago, IL

Simion Filip

Harvard University, Cambridge, MA

Alex Wright

Stanford University, Stanford, CA