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Notes on the universal elliptic KZB connection. (English) Zbl 1439.14044

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.

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
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