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The Chen--Ruan Cohomology of Weighted Projective Spaces |
Canad. J. Math. 59(2007), 981-1007
Published:2007-10-01
Printed: Oct 2007
Printed: Oct 2007
- Yunfeng Jiang
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] |