Pure and Applied Mathematics Quarterly
Volume 16 (2020)
Special Issue: In Honor of Eduard Looijenga, Part 3 of 3
Notes on the universal elliptic KZB connection
Pages: 229 – 312
In this paper, we give an exposition of the elliptic KZB connection over the universal elliptic curve and use it to compute the limit mixed Hodge structure on the unipotent fundamental group of the first order Tate curve. We also give an explicit algebraic formula for the restriction of the elliptic KZB connection to the moduli space of non-zero abelian differentials on an elliptic curve.
Eisenstein series, moduli of elliptic curves, mixed elliptic motives, Hodge theory, algebraic de Rham theory of fundamental groups, elliptic KZB connection
The author was supported in part by the NSF through grants DMS-0706955 and DMS-1005675.
Received 14 June 2016
Accepted 12 March 2017
Published 20 March 2020