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Article Dans Une Revue International Mathematics Research Notices Année : 2015

QUANTUM SERRE IN TERMS OF QUANTUM D-MODULES

Résumé

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
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hal-01101506 , version 1 (08-01-2015)
hal-01101506 , version 2 (12-10-2023)

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Hiroshi Iritani, Etienne Mann, Thierry Mignon. QUANTUM SERRE IN TERMS OF QUANTUM D-MODULES. International Mathematics Research Notices, 2015, 2016 (9), pp.2828-2888. ⟨10.1093/imrn/rnv215⟩. ⟨hal-01101506v1⟩
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