Advances in Theoretical and Mathematical Physics

Volume 20 (2016)

Number 4

Fukaya $A_{\infty}$-categories associated to Lefschetz fibrations. II ½

Pages: 883 – 944

DOI: http://dx.doi.org/10.4310/ATMP.2016.v20.n4.a5

Author

Paul Seidel (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

Abstract

We consider a version of the relative Fukaya category for anti-canonical Lefschetz pencils. There are direct connections between the behaviour of this category and enumerative geometry: some of these are results announced here, others remain conjectural. Among the conjectural goals is a formula for the dependence of the Fukaya category of Calabi–Yau hypersurfaces on the Novikov (area) parameter.

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Published 4 November 2016