Generalized Mari\~no-Vafa Formula and Local Gromov-Witten Theory of   Orbi-curves
  We prove a generalized Mari\~{n}o-Vafa formula for Hodge integrals over $\Mbar_{g, \gamma-\mu}(\cB G)$ with $G$ an arbitrary finite abelian group. Then we use this formula to study the local Gromov-Witten theory of an orbi-curve with cyclic stack points in a Calabi-Yau three-orbifold. 
Zhengyu Zong
math.AG