2025/10/14 by You, Fenglong
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.13027
Given a smooth projective variety X with a smooth anticanonical divisor D, we study mirror symmetry for the log Calabi--Yau pair (X,D) without assuming that D is nef. We consider the mirror proper Landau--Ginzburg model (\check X,W) from the intrinsic mirror construction of Gross--Siebert. We examine the relationship between the regularized quantum period of X and the classical period of W, and identify the discrepancy between them as originating from curve counts in D, governed by the mirror map associated with D. We also obtain an explicit formula for the proper potential W that encodes this discrepancy. In the end, we show that the quantum period, together with the mirror map, gives exactly the same information as the proper potential.