# The algebraic hull of the Kontsevich-Zorich cocycle

## TL;DR

This paper determines the algebraic hull of the Kontsevich-Zorich cocycle over certain invariant subvarieties, leading to finiteness results that enhance understanding of the structure of these mathematical objects.

## Contribution

It computes the algebraic hull of the Kontsevich-Zorich cocycle over GL^+_2(R) invariant subvarieties, providing new finiteness results.

## Key findings

- Algebraic hull computed for the cocycle
- Finiteness results established for invariant subvarieties
- Enhanced understanding of the structure of the Hodge bundle

## Abstract

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