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arXiv · 1604.07888

A-infinity algebras associated with elliptic curves and Eisenstein-Kronecker series

Alexander Polishchuk
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Abstract

We compute the A-infinity structure on the self-Ext algebra of the vector bundle $G$ over an elliptic curve of the form $G=\bigoplus_{i=1}^r P_i\oplus \bigoplus_{j=1}^s L_j$, where $(P_i)$ and $(L_j)$ are line bundles of degrees 0 and 1, respectively. The answer is given in terms of Eisenstein-Kronecker numbers $(e^*_{a,b}(z,w))$. The A-infinity constraints lead to quadratic polynomial identities between these numbers, allowing to express them in terms of few ones. Another byproduct of the calculation is the new representation for $e^*_{a,b}(z,w)$ by rapidly converging series.

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Alexander Polishchuk. 2016-04-26. A-infinity algebras associated with elliptic curves and Eisenstein-Kronecker series. https://arxiv.org/abs/1604.07888

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