|
|||||
|
|
|
|
|
|
|
|
|
The
local Gromov–Witten invariants of configurations of rational
curves
Dagan Karp, Chiu-Chu Melissa Liu and Marcos Mariño |
|
Geometry & Topology 10 (2006) 115–168
|
|
arXiv: math.AG/0506488 |
Abstract |
|
We compute the local Gromov–Witten invariants of certain configurations of rational curves in a Calabi–Yau threefold. These configurations are connected subcurves of the “minimal trivalent configuration”, which is a particular tree of ’s with specified formal neighborhood. We show that these local invariants are equal to certain global or ordinary Gromov–Witten invariants of a blowup of at points, and we compute these ordinary invariants using the geometry of the Cremona transform. We also realize the configurations in question as formal toric schemes and compute their formal Gromov–Witten invariants using the mathematical and physical theories of the topological vertex. In particular, we provide further evidence equating the vertex amplitudes derived from physical and mathematical theories of the topological vertex. |
Keywords
Gromov–Witten invariants, Calabi–Yau threefolds,
topological vertex
|
Mathematical Subject Classification 2000
Primary: 14N35
Secondary: 53D45
|
References |
Forward citations |
Publication
Received: 23 August 2005
Accepted: 25 November 2005
Published: 7 March 2006
Proposed: Jim Bryan
Seconded: Paul Goerss, Eleny Ionel
|
Authors |
| Dagan Karp | |
| Department of Mathematics University of California at Berkeley California 94720-3840 USA |
|
| Chiu-Chu Melissa Liu | |
| Department of Mathematics Northwestern University Evanston Illinois 60208-2370 USA |
|
| Marcos Mariño | |
| Department of Physics CERN Geneva 23 CH-1211 Switzerland |
|
|
