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We give an interpretation of quantum Serre of Coates and Givental as aduality of twisted quantum D-modules. This interpretation admits anon-equivariant limit, and we obtain a precise relationship among (1) thequantum 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^\vee over X,and (3) the quantum D-module of a submanifold Z\subset X cut out by a regularsection of E. When E is the anticanonical line bundle K_X^{-1}, we identifythese twisted quantum D-modules with second structure connections withdifferent parameters, which arise as Fourier-Laplace transforms of the quantumD-module of X. In this case, we show that the duality pairing is identifiedwith Dubrovin's second metric (intersection form).

Quantum Serre theorem as a duality between quantum D-modules