Hodge structures Orbifold hodge numbers and a correspondence in   Quasitoric Orbifolds
  We give hodge structures on quasitoric orbifolds. We define orbifold hodge numbers and show a correspondence of orbifold hodge numbers for crepant resolutions of quasitoric orbifolds. In short we extend hodge structures to a non complex setting . 
Saibal Ganguli
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