• Ganguli, Saibal (Harish-Chandra Research Institute)
  • Received : 2016.01.04
  • Published : 2017.05.01


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 almost complex setting.


Hodge structures;orbifold;quasitoric;projective toric


  1. W. L. Baily, Jr., The decomposition theorem for V-manifolds, Amer. J. Math. 78 (1956), no. 4, 862-888.
  2. V. V. Batyrev and D. I. Dais, Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry, Topology 35 (1996), no. 4, 901-929.
  3. V. M. Buchstaber and T. E. Panov, Torus actions and their applications in topology and combinatorics, University Lecture Series 24, American Mathematical Society, Providence, RI, 2002.
  4. W. Chen and Y. Ruan, A new cohomology theory of orbifold, Comm. Math. Phys. 248 (2004), no. 1, 1-31.
  5. C.-H. Cho and M. Poddar, Holomorphic orbidiscs and Lagrangian Floer cohomology of symplectic toric orbifolds, J. Differential Geom. 98 (2014), no. 1, 21-116.
  6. M. W. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991), no. 2, 417-451.
  7. S. Ganguli, Mckay corespondence in quasitoric orbifolds, arXiv:1308.3949.
  8. S. Ganguli and M. Poddar, Blowdowns and McKay correspondence on four dimensional quasitoric orbifolds, Osaka J. Math. 50 (2013), no. 2, 397-415.
  9. S. Ganguli and M. Poddar, Almost complex structure, blowdowns and McKay correspondence in quasitoric orbifolds, Osaka J. Math. 50 (2013), no. 4, 977-1005.
  10. E. Lerman and S. Tolman, Hamiltonian torus actions on symplectic orbifolds and toric varieties, Trans. Amer. Math. Soc. 349 (1997), no. 10, 4201-4230.
  11. E. Lupercio and M. Poddar, The global McKay-Ruan correspondence via motivic integration, Bull. London Math. Soc. 36 (2004), no. 4, 509-515.
  12. C. Peters and J. Steenbrink, Mixed Hodge Structures, A Series of Modern Surveys in Mathematics, Vol. 52, Springer, 2008.
  13. M. Poddar, Orbifold cohomology group of toric varieties, Orbifolds in Mathematics and Physics (Madison, WI, 2001), 223-231, Contemp. Math., 310, Amer. Math. Soc., Providence, RI, 2002.
  14. M. Poddar, Orbifold Hodge numbers of Calabi-Yau hypersurfaces, arxiv:01071552v.
  15. M. Poddar and S. Sarkar, On quasitoric orbifolds, Osaka J. Math. 47 (2010), no. 4, 1055-1076.
  16. T. Yasuda, Twisted jets, motivic measures and orbifold cohomology, Compos. Math. 140 (2004), no. 2, 396-422.
  17. T. Yasuda, Motivic integration over Deligne-Mumford stacks, Adv. Math. 207 (2006), no. 2, 707-761.
  18. E. Zaslow, Topological orbifold models and quantum cohomology rings, Comm. Math. Phys. 156 (1993), no. 2, 301-331.