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Quantum Cohomology and Periods

Hiroshi Iritani (2011)

Annales de l’institut Fourier

In a previous paper, the author introduced an integral structure in quantum cohomology defined by the K -theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle to the previous results, we find an explicit relationship between solutions to the quantum differential equation of toric complete intersections and the periods (or oscillatory integrals) of their mirrors. We describe in detail the mirror isomorphism of...

Quartic del Pezzo surfaces over function fields of curves

Brendan Hassett, Yuri Tschinkel (2014)

Open Mathematics

We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of sections to the fibration, and mappings to the intermediate Jacobian of the total space. We exhibit examples where these are birational, which has applications to arithmetic questions, especially over finite fields.

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