Quantum D-modules and generalized mirror transformations

Details Quantum D-modules and generalized mirror transformations Quantum D-modules and generalized mirror transformations

2004-11-05

arxiv.org/abs/math/0411111v5

Topology 47 (2008) no.4, pp.225--276

Mathematics

Differential Geometry

54 pages; v2: corrected typos; v3: added reference; v4: corrected errors in the proof of the main theorem; v5: major revision.

Scientific paper

10.1016/j.top.2007.07.001

In the previous paper, the author defined equivariant Floer cohomology for a complete intersection in a toric variety and showed that it is isomorphic to the small quantum D-module after a mirror transformation when the first Chern class c_1(M) of the tangent bundle is nef. In this paper, even when c_1(M) is not nef, we show that the equivariant Floer cohomology reconstructs the big quantum D-module under certain conditions on the ambient toric variety. The proof is based on a mirror theorem by Coates and Givental. The reconstruction procedure here gives a generalized mirror transformation first observed by Jinzenji in low degrees.

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