2014/12/15 by Hiroshi Iritani, Etienne Mann, Thierry Mignon +1 · 1 voice · 1 citation
Mathematics · #Advanced Operator Algebra Research #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.1093/imrn/rnv215
openalex publication_date 2014/12/15 · arxiv published 2014/12/15 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an interpretation of quantum Serre of Coates and Givental as a duality of twisted quantum D-modules. This interpretation admits a non-equivariant limit, and we obtain a precise relationship among (1) the quantum D-module of X twisted by a convex vector bundle E and the Euler class, (2) the quantum D-module of the total space of the dual bundle E ∨ → X, and (3) the quantum D-module of a submanifold Z ⊂ X cut out by a regular section of E. When E is the anticanonical line bundle K −1 X , we identify these twisted quantum D-modules with second structure connections with different parameters, which arise as Fourier-Laplace transforms of the quantum D-module of X. In this case, we show that the duality pairing is identified with Dubrovin's second metric. CONTENTS