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Intrinsic Mirror Symmetry and Quantum Periods of Fano Varieties

For a Fano variety and a reduced anticanonical divisor forming a log Calabi-Yau pair, the Gross-Siebert intrinsic mirror algebra contains a distinguished superpotential whose classical periods equal the regularized quantum periods of the Fano variety. Students learn how this identification produces canonical Landau-Ginzburg mirrors, proves integrality of regularized quantum periods, and yields Newton-Okounkov bodies and toric degenerations of the variety from seeds of a cluster structure.

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QUANTUM PERIODS, TORIC DEGENERATIONS AND INTRINSIC MIRROR SYMMETRY SAMUEL JOHNSTON Abstract. Given

The regularized quantum period of a smooth Fano variety is a generating series of its genus-zero Gromov-Witten invariants, and Fano/Landau-Ginzburg mirror symmetry predicts it equals an oscillatory i…