The classical periods of the intrinsic mirror algebra of a log Calabi-Yau Fano pair reproduce the regularized quantum periods of the Fano variety.
Theta functions, broken lines and 2-marked log Gromov-Witten invariants
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abstract
Theta functions were defined for varieties with effective anticanonical divisor and are related to certain punctured Gromov-Witten invariants. In this paper we show that in the case of a log Calabi-Yau surface (X,D) with smooth very ample anticanonical divisor we can circumvent the notion of punctured Gromov-Witten invariants and relate theta functions and their multiplicative structure to certain 2-marked log Gromov-Witten invariants. This is a natural extension of the correspondence between wall functions and 1-marked log Gromov-Witten invariants.
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Quantum periods, toric degenerations and intrinsic mirror symmetry
The classical periods of the intrinsic mirror algebra of a log Calabi-Yau Fano pair reproduce the regularized quantum periods of the Fano variety.