Floer cohomology and pencils of quadrics
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.
Keywords
Cite
@article{arxiv.1006.1099,
title = {Floer cohomology and pencils of quadrics},
author = {Ivan Smith},
journal= {arXiv preprint arXiv:1006.1099},
year = {2011}
}
Comments
70 pages, 7 figures. Version 2: corrections and simplifications to the finite determinacy and blowing up arguments; general re-organisation and some auxiliary material removed to appear elsewhere. Version 3: choice of symplectic forms clarified, various typoes corrected