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The Chen–Ruan Cohomology of Weighted Projective Spaces

  • Yunfeng Jiang (a1)
Abstract

In this paper we study the Chen–Ruan cohomology ring of weighted projective spaces. Given a weighted projective space we determine all of its twisted sectors and the corresponding degree shifting numbers. The main result of this paper is that the obstruction bundle over any 3-multisector is a direct sum of line bundles which we use to compute the orbifold cup product. Finally we compute the Chen–Ruan cohomology ring of weighted projective space

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References
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[1] Amrami, A. A., Cohomological study of weighted projective space. In: Algebraic Geometry. Lecture Notes in Pure and Applied Mathematics 193, Marcel Dekker, New York, 1997.
[2] Atiyah, M. and Bott, R., The moment map and equivariant cohomology. Topology 23(1984), no. 1, 128.
[3] Borisov, L., Chen, L. and Smith, G., The orbifold Chow ring of toric Deligne-Mumford stacks. J. Amer. Math. Soc. 18(2005), no.1, 193–215.
[4] Conrads, H., Weighted projective spaces and reflexive simplices. Manuscripta Math. 107(2002), no. 2, 215227.
[5] Chen, W. and Ruan, Y., A new cohomology theory for orbifolds. Comm. Math. Phys. 248(2004), no. 1, 131.
[6] Dixon, L., Harvey, J., Vafa, C., and Witten, E., Strings on orbifolds. I. Nuclear Phys. B 261(1985), 678686.
[7] Dixon, L., Harvey, J., Vafa, C., and Witten, E., Strings on orbifolds. II. Nuclear Phys. B 274(1986), 285314.
[8] Cox, D. and Katz, S., Mirror Symmetry and Algebraic Geometry. Mathematical Surveys and Monographs 68, American Mathematical Society, Providence, RI, 1999.
[9] Fulton, W., Introduction to toric varieyies, Annals of Mathematics Studies 131, Princeton University Press, Princeton, NJ, 1993.
[10] Godinho, L., Blowing up symplectic orbifolds. Ann. Global Anal. Geom. 20(2001), no. 2, 117162.
[11] Kawaski, T., Cohomology of twisted projective spaces and lens complexes.. Math. Ann. 206(1973), 243248.
[12] Kawaski, T., The signature theorem for V-manifolds. Topology 17(1978), 7583.
[13] Kobayashi, S. and Nomizu, K., Foundations of differential geometry. Vol. I, Interscience Publishers, New York, 1963.
[14] Oda, T., Covex Bodies and Algebraic Geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete 15, Springer-Verlag, Berlin, 1988.
[15] Poddar, M., Orbifold Hodge numbers of Calabi-Yau hypersurfaces. Pacific J. Math. 208(2003), no. 1, 151167.
[16] Park, B. D. and Poddar, M., The Chen–Ruan cohomology ring of mirror quintic, arXiv:math.AG/0210185.
[17] Ruan, Y., Cohomology ring of crepant resolution of orbifolds. arXiv:math.AG/0108195.
[18] Zaslow, E., Topological orbifold models and quantum cohomology rings. Comm. Math. Phys. 156(1993), no. 2, 301331.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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