Quantum Serre theorem as a duality between quantum D-modules
Abstract
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^\vee over X, and (3) the quantum D-module of a submanifold Z\subset X cut out by a regular section of E. When E is the anticanonical line bundle K_X^{-1}, 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 (intersection form).
Cite
@article{arxiv.1412.4523,
title = {Quantum Serre theorem as a duality between quantum D-modules},
author = {Hiroshi Iritani and Etienne Mann and Thierry Mignon},
journal= {arXiv preprint arXiv:1412.4523},
year = {2016}
}
Comments
40 pages, v2: the title has changed, exposition improved and references added, accepted for publication in International Mathematics Research Notices