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arXiv · 1006.1099

Floer cohomology and pencils of quadrics

Ivan Smith
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Abstract

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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Ivan Smith. 2011-10-13. Floer cohomology and pencils of quadrics. https://arxiv.org/abs/1006.1099

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