The crepant resolution conjecture. (English) Zbl 1198.14053
Abramovich, D. (ed.) et al., Algebraic geometry, Seattle 2005. Proceedings of the 2005 Summer Research Institute, Seattle, WA, USA, July 25–August 12, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4702-2/hbk; 978-0-8218-4057-3/set). Proceedings of Symposia in Pure Mathematics 80, Pt. 1, 23-42 (2009).
The authors formulate a conjectural equivalence between Gromov-Witten theories of the orbifold and the resolution. Namely, their conjecture relates the two potential functions \(F^{Y}\) and \(F^{\chi}\) where \(Y\) is a crepant resolution of the orbifold \(\chi\). They also prove the conjecture for equivariant GW theories for \(\text{Sym}^{n}\mathbb{C}^{2}\) and \(\text{Hilb}^{n}\mathbb{C}^{2}\).
For the entire collection see [Zbl 1158.14003].
For the entire collection see [Zbl 1158.14003].
Reviewer: Vehbi Emrah Paksoy (Ft. Lauderdale)
MSC:
| 14N35 | Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) |
| 14E15 | Global theory and resolution of singularities (algebro-geometric aspects) |
