## Journal of Differential Geometry

### Generalized Mariño-Vafa formula and local Gromov-Witten theory of orbi-curves

Zhengyu Zong

#### Abstract

We prove a generalized Mariño-Vafa formula for Hodge integrals over $\overline{\mathcal{M}}_{g, \gamma - \mu} (\mathcal{B}G)$ with $G$ an arbitrary finite abelian group. This formula can be viewed as a formula for the one-leg orbifold Gromov-Witten vertex where the leg is effective. We will prove the orbifold Gromov-Witten/Donaldson-Thomas correspondence between our formula and the formula for the orbifold DT vertex in J. Bryan, C. Cadman & B. Young, The orbifold topological vertex. We will also use this formula to study the local Gromov-Witten theory of an orbi-curve with cyclic stack points in a Calabi-Yau three-orbifold.

#### Article information

Source
J. Differential Geom., Volume 100, Number 1 (2015), 161-190.

Dates
First available in Project Euclid: 24 March 2015

https://projecteuclid.org/euclid.jdg/1427202767

Digital Object Identifier
doi:10.4310/jdg/1427202767

Mathematical Reviews number (MathSciNet)
MR3326577

Zentralblatt MATH identifier
1344.14033

#### Citation

Zong, Zhengyu. Generalized Mariño-Vafa formula and local Gromov-Witten theory of orbi-curves. J. Differential Geom. 100 (2015), no. 1, 161--190. doi:10.4310/jdg/1427202767. https://projecteuclid.org/euclid.jdg/1427202767