Quantum differential systems and some applications to mirror symmetry

Details Quantum differential systems and some applications to mirror symmetry Quantum differential systems and some applications to mirror symmetry

2012-03-27

arxiv.org/abs/1203.5920v1

Mathematics

Algebraic Geometry

81 pages

Scientific paper

We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a good framework in order to generalize the construction of the rational structure on the A-side given by Katzarkov, Kontsevitch and Pantev for the projective spaces. As an application, we compute the rational structure obtained in this way on the orbifold cohomology of weighted projective spaces. As an example we also calculate, using quantum differential systems, a mirror partner of the Hirzebruch surface.

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