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

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

2001-07-27

arxiv.org/abs/math/0107194v3

Mathematics

Algebraic Geometry

latex, 16 pages, a misprint corrected, references updated

Scientific paper

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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