Massey and Fukaya products on elliptic curves

Universal triple Massey products on elliptic curves and Hecke's indefinite theta series

Generalizing math.AG/0003076 we express universal triple Massey products between line bundles on elliptic curves in terms of Hecke's indefinite theta series. We show that all Hecke's indefinite theta series arise in this way.

Massey products for elliptic curves of rank 1

For an elliptic curve over Q of analytic rank 1, we use the level-two Selmer variety and secondary cohomology products to find explicit analytic defining equations for global integral points inside the set of p-adic points.

Massey 积与椭圆曲线

Massey products and elliptic curves

本文研究完美域上绝对不可约光滑射影曲线中系数为 $\mathbb{Z}/\ell$ 的高阶 Massey 积消失问题，并完整刻画椭圆曲线上三重 Massey 积非消失的条件。

Classical Yang-Baxter equation and the $A_{\infty}$-constraint

We show that elliptic solutions of the classical Yang-Baxter equation can be obtained from triple Massey products on elliptic curve. We introduce the associative version of this equation which has two spectral parameters and construct its elliptic solutions. We also study some degenerations of these solutions.

Homological mirror symmetry for elliptic Hopf surfaces

We show homological mirror symmetry results relating coherent analytic sheaves on some complex elliptic surfaces and objects of certain Fukaya categories. We first define the notion of a non-algebraic Landau-Ginzburg model on $\mathbb{R} \times S^1$ and its associated Fukaya category, and show that non-Kähler sur-faces obtained by performing two logarithmic transformations to the product of the projective plane and an elliptic curve have non-algebraic Landau-Ginzburg models as their mirror spaces; this class of surface includes the classical Hopf surface $S^1\times S^3$ and other elliptic prim…

M. P. Appell's function and vector bundles of rank 2 on elliptic curve

This paper is devoted to the function introduced by M. P. Appell in connection with decomposition of elliptic functions of the third kind into simple elements. We show that this function (which appeared as a Fukaya triple product in math.AG/9803017) is related to global sections of rank-2 vector bundles on elliptic curves. We derive analogues of theta-identities for this function and prove the divisibility property for the action of modular group which should be considered as a replacement for functional equation.