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

2001/07/27 by Alexander Polishchuk, Polishchuk, Alexander
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0107194

latex, 16 pages, a misprint corrected, references updated

arxiv created 2002/07/29 · arxiv updated 2009/11/30

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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