Quantum Cohomology and Periods

Hiroshi Iritani[1]

  • [1] Kyoto University Department of Mathematics Kitashirakawa-Oiwake-cho Sakyo-ku, Kyoto, 606-8502 (Japan)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 7, page 2909-2958
  • ISSN: 0373-0956

Abstract

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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 variations of integral Hodge structure for a mirror pair of Calabi-Yau hypersurfaces (Batyrev’s mirror).

How to cite

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Iritani, Hiroshi. "Quantum Cohomology and Periods." Annales de l’institut Fourier 61.7 (2011): 2909-2958. <http://eudml.org/doc/275478>.

@article{Iritani2011,
abstract = {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 variations of integral Hodge structure for a mirror pair of Calabi-Yau hypersurfaces (Batyrev’s mirror).},
affiliation = {Kyoto University Department of Mathematics Kitashirakawa-Oiwake-cho Sakyo-ku, Kyoto, 606-8502 (Japan)},
author = {Iritani, Hiroshi},
journal = {Annales de l’institut Fourier},
keywords = {quantum cohomology; mirror symmetry; Gamma class; $K$-theory; period; oscillatory integral; variation of Hodge structure; GKZ system; toric variety; orbifold; gamma class; -theory},
language = {eng},
number = {7},
pages = {2909-2958},
publisher = {Association des Annales de l’institut Fourier},
title = {Quantum Cohomology and Periods},
url = {http://eudml.org/doc/275478},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Iritani, Hiroshi
TI - Quantum Cohomology and Periods
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 7
SP - 2909
EP - 2958
AB - 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 variations of integral Hodge structure for a mirror pair of Calabi-Yau hypersurfaces (Batyrev’s mirror).
LA - eng
KW - quantum cohomology; mirror symmetry; Gamma class; $K$-theory; period; oscillatory integral; variation of Hodge structure; GKZ system; toric variety; orbifold; gamma class; -theory
UR - http://eudml.org/doc/275478
ER -

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