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Fano mirror periods from the Frobenius structure conjecture
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The Fano classification program proposed by Coates-Corti-Galkin-Golyshev-Kasprzyk is based on the mirror symmetry prediction that the regularized quantum period of a Fano should be equivalent to the classical period of its mirror Landau-Ginzburg potential. We prove that this mirror equivalence follows from versions of the Frobenius structure conjecture of Gross-Hacking-Keel. We also find that the regularized quantum period, which is defined in terms of descendant Gromov-Witten numbers, is in fact given by certain naive curve counts.
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Cited by 2 Pith papers
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On Arithmetic Mirror Symmetry for smooth Fano fourfolds
An explicit class of tempered Laurent polynomials is defined that contains LG models for Fano threefolds and checked Fano fourfolds, enabling two new examples of Arithmetic Mirror Symmetry correspondences via Kerr's p...
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On Arithmetic Mirror Symmetry for smooth Fano fourfolds
An explicit class of tempered Laurent polynomials is introduced that includes Landau-Ginzburg models for smooth Fano threefolds and various Fano fourfolds, enabling two new examples of arithmetic mirror symmetry corre...
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