Mirror symmetry of variations of Hodge structures for Fano varieties
Let be a Fano variety, and let be a one-parameter family. The Picard--Fuchs -module of is the differential -module governing the periods of the family, while the regularized quantum -module is the regularized differential system associated with the quantum cohomology of .
Mirror symmetry of variations of Hodge structures. For any Fano variety there exists a one-parameter family
whose Picard--Fuchs -module is isomorphic to a regularized quantum -module for .
This conjecture proposes a mirror-symmetric realization of the quantum differential system of every Fano variety as the Picard--Fuchs system of a one-parameter family. The source provides no evidence of resolution, so the conjecture remains open.
References
Primary source
Nathan Owen Ilten, Jacob Lewis and Victor Przyjalkowski, “Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models”, arXiv:1102.4664 (2012).
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