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# The Chen--Ruan Cohomology of Weighted Projective Spaces

Published:2007-10-01
Printed: Oct 2007
• Yunfeng Jiang
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## Abstract

In this paper we study the Chen--Ruan cohomology ring of weighted projective spaces. Given a weighted projective space ${\bf P}^{n}_{q_{0}, \dots, q_{n}}$, 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\nobreakdash-multi\-sector 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 ${\bf P}^{5}_{1,2,2,3,3,3}$.
 Keywords: Chen--Ruan cohomology, twisted sectors, toric varieties, weighted projective space, localization
 MSC Classifications: 14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45] 53D45 - Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]

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