The Local Gromov–Witten Invariants of Configurations of Rational Curves

Authors

Dagan Karp, Harvey Mudd CollegeFollow
Chiu-Chu Melissa Liu, Northwestern University
Marcos Mariño, CERN

Document Type

Article

Department

Mathematics (HMC)

Publication Date

3-2006

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 ℙ¹’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 ℙ³ 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.

Comments

Archived with permission from Geometry and Topology.

Rights Information

© 2006 Geometry and Topology

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.2140/gt.2006.10.115

Recommended Citation

Karp, Dagan, Chiu-Chu Melissa Liu and Marcos Mariño. "The local Gromov-Witten invariants of configurations of rational curves." Geometry & Topology. 10 (2006) 115-168.