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• W1817966437 abstract "The universal elliptic KZB equation is the integrable connection on the pro-vector bundle over M_{1,2} whose fiber over the point corresponding to the elliptic curve E and a non-zero point x of E is the unipotent completion of pi_1(E-{0},x). This was written down independently by Calaque, Enriquez and Etingof (arXiv:math/0702670), and by Levin and Racinet (arXiv:math/0703237). It generalizes the KZ-equation in genus 0. These notes are in four parts. The first two parts provide a detailed exposition of this connection (following Levin-Racinet); the third is a leisurely exploration of the connection in which, for example, we compute the limit mixed Hodge structure on the unipotent fundamental group of the Tate curve minus its identity. In the fourth part we elaborate on ideas of Levin and Racinet and explicitly compute the connection over the moduli space of elliptic curves with a non-zero abelian differential, showing that it is defined over Q." @default.
• W1817966437 created "2016-06-24" @default.
• W1817966437 creator A5020592885 @default.
• W1817966437 date "2020-01-01" @default.
• W1817966437 modified "2023-09-30" @default.
• W1817966437 title "Notes on the universal elliptic KZB connection" @default.
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• W1817966437 doi "https://doi.org/10.4310/pamq.2020.v16.n2.a2" @default.
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