Stringy Hodge numbers of Pfaffian double mirrors and Homological Projective Duality

TL;DR

This paper investigates the stringy Hodge numbers of Pfaffian double mirrors, introduces modified stringy $E$-functions, and explores their relations to categorical crepant resolutions, advancing understanding in mirror symmetry and algebraic geometry.

Contribution

It generalizes previous work by Borisov and Libgober, introduces a modified version of stringy $E$-functions, and predicts Lefschetz decompositions in Pfaffian varieties.

Findings

Relations between modified stringy $E$-functions on dual sides

Numerical predictions for Lefschetz decompositions

Extension of stringy Hodge number calculations to Pfaffian double mirrors

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.