Quantum periods for 3dimensional Fano manifoldsTools Coates, Tom and Corti, Alessio and Galkin, Sergey and Kasprzyk, Alexander M. (2016) Quantum periods for 3dimensional Fano manifolds. Geometry & Topology, 20 (1). pp. 103256. ISSN 13640380 This is the latest version of this item.
Official URL: http://msp.org/gt/2016/201/p03.xhtml
AbstractThe quantum period of a variety X is a generating function for certain GromovWitten invariants of X which plays an important role in mirror symmetry. In this paper we compute the quantum periods of all 3dimensional Fano manifolds. In particular we show that 3dimensional 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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