Quantum periods for 3-dimensional Fano manifolds
Coates, Tom and Corti, Alessio and Galkin, Sergey and Kasprzyk, Alexander M. (2016) Quantum periods for 3-dimensional Fano manifolds. Geometry & Topology, 20 (1). pp. 103-256. ISSN 1364-0380
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The quantum period of a variety X is a generating function for certain Gromov-Witten invariants of X which plays an important role in mirror symmetry. In this paper we compute the quantum periods of all 3-dimensional Fano manifolds. In particular we show that 3-dimensional Fano manifolds with very ample anticanonical bundle have mirrors given by a collection of Laurent polynomials called Minkowski polynomials. This was conjectured in joint work with Golyshev. It suggests a new approach to the classification of Fano manifolds: by proving an appropriate mirror theorem and then classifying Fano mirrors.
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