Floer cohomology and pencils of quadrics

Details Floer cohomology and pencils of quadrics Floer cohomology and pencils of quadrics

2010-06-06

arxiv.org/abs/1006.1099v3

Mathematics

Symplectic Geometry

70 pages, 7 figures. Version 2: corrections and simplifications to the finite determinacy and blowing up arguments; general re

Scientific paper

There is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces. We investigate symplectic aspects of this relationship, with a view to applications in low-dimensional topology. We construct a derived equivalence between the Fukaya category of a curve and the nilpotent summand of the Fukaya category of the associated complete intersection of two quadrics. This essentially determines the instanton Floer homology of a 3-manifold fibred by genus two curves.

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