Open Access
2009 The quantum orbifold cohomology of weighted projective spaces
Tom Coates, Alessio Corti, Yuan-Pin Lee, Hsian-Hua Tseng
Author Affiliations +
Acta Math. 202(2): 139-193 (2009). DOI: 10.1007/s11511-009-0035-x


We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental’s heuristic argument, which relates small quantum cohomology to S1-equivariant Floer cohomology of loop space, to weighted projective spaces and use this to conjecture an explicit formula for the small J-function, a generating function for certain genus-zero Gromov–Witten invariants. We prove this conjecture using a method due to Bertram. This provides the first non-trivial example of a family of orbifolds of arbitrary dimension for which the small quantum orbifold cohomology is known. In addition we obtain formulas for the small J-functions of weighted projective complete intersections satisfying a combinatorial condition; this condition naturally singles out the class of orbifolds with terminal singularities.


Download Citation

Tom Coates. Alessio Corti. Yuan-Pin Lee. Hsian-Hua Tseng. "The quantum orbifold cohomology of weighted projective spaces." Acta Math. 202 (2) 139 - 193, 2009.


Received: 26 October 2006; Published: 2009
First available in Project Euclid: 31 January 2017

zbMATH: 1213.53106
MathSciNet: MR2506749
Digital Object Identifier: 10.1007/s11511-009-0035-x

Rights: 2009 © Institut Mittag-Leffler

Vol.202 • No. 2 • 2009
Back to Top