Hain, Richard Notes on the universal elliptic KZB connection. (English) Zbl 1439.14044 Pure Appl. Math. Q. 16, No. 2, 229-312 (2020). Summary: 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. Cited in 13 Documents MSC: 14D07 Variation of Hodge structures (algebro-geometric aspects) 11F23 Relations with algebraic geometry and topology 14H10 Families, moduli of curves (algebraic) 14H52 Elliptic curves Keywords:Eisenstein series; moduli of elliptic curves; mixed elliptic motives; Hodge theory; algebraic de Rham theory of fundamental groups; elliptic KZB connection PDFBibTeX XMLCite \textit{R. Hain}, Pure Appl. Math. Q. 16, No. 2, 229--312 (2020; Zbl 1439.14044) Full Text: DOI arXiv