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The Chen–Ruan Cohomology of Weighted Projective Spaces

Published online by Cambridge University Press:  20 November 2018

Yunfeng Jiang
Yunfeng Jiang*
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2 email: jiangyf@math.ubc.ca
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Abstract

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In this paper we study the Chen–Ruan cohomology ring of weighted projective spaces. Given a weighted projective space ${{\mathbf{P}}^{n}}_{{{q}_{0}},\ldots ,{{q}_{n}}}$, 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 $\mathbf{P}_{1,\,2,\,2,\,3,3,\,{{3}^{\centerdot }}}^{5}$.

Keywords

14N3553D45Chen–Ruan cohomologytwisted sectorstoric varietiesweighted projective spacelocalization
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 5 , 01 October 2007 , pp. 981 - 1007
Copyright
Copyright © Canadian Mathematical Society 2007

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