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An integral structure in quantum cohomology and mirror symmetry for toric orbifolds

Authors
Journal
Advances in Mathematics
0001-8708
Publisher
Elsevier
Publication Date
Volume
222
Issue
3
Identifiers
DOI: 10.1016/j.aim.2009.05.016
Keywords
  • Quantum Cohomology
  • Variation Of Hodge Structures
  • Semi-Infinite Variation Of Hodge Structures
  • Mirror Symmetry
  • Landau–Ginzburg Model
  • Toric Deligne–Mumford Stack
  • Orbifold
  • Orbifold Quantum Cohomology
  • Crepant Resolution Conjecture
  • Ruan'S Conjecture
  • K-Theory
  • Mckay Correspondence
  • Oscillatory Integral
  • Hypergeometric Function
  • Gkz-System
  • Singularity Theory
  • Gamma Class
Disciplines
  • Physics

Abstract

Abstract We introduce an integral structure in orbifold quantum cohomology associated to the K-group and the Γ ˆ -class. In the case of compact toric orbifolds, we show that this integral structure matches with the natural integral structure for the Landau–Ginzburg model under mirror symmetry. By assuming the existence of an integral structure, we give a natural explanation for the specialization to a root of unity in Y. Ruan's crepant resolution conjecture [Yongbin Ruan, The cohomology ring of crepant resolutions of orbifolds, in: Contemp. Math., vol. 403, Amer. Math. Soc., Providence, RI, 2006, pp. 117–126].

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