Stringy Hodge numbers of Pfaffian double mirrors and Homological Projective Duality

Abstract: We study the stringy Hodge numbers of Pfaffian double mirrors, generalizing previous results of Borisov and Libgober. In the even-dimensional cases, we introduce a modified version of stringy $E$-functions and obtain interesting relations between the modified stringy $E$-functions on the two sides. We use them to make numerical predictions on the Lefschetz decompositions of the categorical crepant resolutions of Pfaffian varieties.