Resumen de AA∞∞ -algebras associated with elliptic curves and Eisenstein–Kronecker series

Alexander Polishchuk

• We compute the A∞ -structure on the self- Ext algebra of the vector bundle G over an elliptic curve of the form G=⨁ri=1Pi⊕⨁sj=1Lj , where (Pi) and (Lj) 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∞ -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.