On the monodromy of the Hitchin connection

TL;DR

This paper provides an example of a family of genus g > 1 curves where the monodromy of the Hitchin connection exhibits elements of infinite order, revealing new insights into its structure.

Contribution

It demonstrates that for certain levels, the monodromy representation of the Hitchin connection can contain elements of infinite order, challenging previous assumptions.

Findings

Monodromy contains elements of infinite order for specific levels.

Provides explicit examples for genus g > 1.

Enhances understanding of Hitchin connection's monodromy structure.

Abstract

For any genus g > 1 we give an example of a family of smooth complex projective curves of genus g such that the image of the monodromy representation of the Hitchin connection on the sheaf of generalized SL(2)-theta functions of level l different from 1,2,4 and 8 contains an element of infinite order.