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Triple Massey products on curves, Fay's trisecant identity and tangents to the canonical embedding

Alexander Polishchuk
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Abstract

We show that Fay's trisecant identity follows from the A_{infinity}-constraint between certain triple Massey products in the derived category of coherent sheaves on a curve. We also deduce the matrix analogue of this identity that can be conveniently formulated using quasideterminants of matrices with non-commuting entries. On the other hand, looking at more special triple Massey products we derive a formula for the tangent line to a canonically embedded curve at a given point.

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Alexander Polishchuk. 2002-07-29. Triple Massey products on curves, Fay's trisecant identity and tangents to the canonical embedding. https://arxiv.org/abs/math/0107194

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