The number of ramified covering of a Riemann surface by Riemann surface

Abstract

Interpreting the number of ramified covering of a Riemann surface by Riemann surfaces as the relative Gromov-Witten invariants and applying a gluing formula, we derive a recursive formula for the number of ramified covering of a Riemann surface by Riemann surface with elementary branch points and prescribed ramification type over a special point.

LaTex, 14 pages

References in corpus (2)

• Large $N$ Phases of Chiral QCD_2
• Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds I

Cited by in corpus (8)

• The Hurwitz Enumeration Problem of Branched Covers and Hodge Integrals
• Relative orbifold Gromov-Witten theory and degeneration formula
• Formulae of one-partition and two-partition Hodge integrals
• Lectures on the ELSV formula
• Genus Expanded Cut-and-Join operators and generalized Hurwtiz numbers
• On the lower bounds for real double Hurwitz numbers
• Ruan's Conjecture on Singular symplectic flops
• Shifted genus expanded ${\mathcal{W}}_{\infty }$ algebra and shifted Hurwtiz numbers