Duke Mathematical Journal

Curves in Calabi-Yau threefolds and topological quantum field theory

Jim Bryan and Rahul Pandharipande

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Abstract

We continue our study of the local Gromov-Witten invariants of curves in Calabi-Yau threefolds.

We define relative invariants for local theory which give rise to a (1+1)-dimensional topological quantum field theory (TQFT) taking values in the ring $\mathbb{Q}[[t]]$. The associated Frobenius algebra over $\mathbb{Q}[[t]]$ is semisimple. Consequently, we obtain a structure result for the local invariants. As an easy consequence of our structure formula, we recover the closed formulas for the local invariants in the case where either the target genus or the degree equals 1.

Article information

Source
Duke Math. J. Volume 126, Number 2 (2005), 369-396.

Dates
First available: 21 January 2005

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1106332724

Digital Object Identifier
doi:10.1215/S0012-7094-04-12626-0

Mathematical Reviews number (MathSciNet)
MR2115262

Zentralblatt MATH identifier
1084.14053

Subjects
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]

Citation

Bryan, Jim; Pandharipande, Rahul. Curves in Calabi-Yau threefolds and topological quantum field theory. Duke Mathematical Journal 126 (2005), no. 2, 369--396. doi:10.1215/S0012-7094-04-12626-0. http://projecteuclid.org/euclid.dmj/1106332724.


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