Geometry of meromorphic functions and intersections on moduli spaces of curves

Abstract

In this paper we study relations between intersection numbers on moduli spaces of curves and Hurwitz numbers. First, we prove two formulas expressing Hurwitz numbers of (generalized) polynomials via intersections on moduli spaces of curves. Then we show, how intersection numbers can be expressed via Hurwitz numbers. And then we obtain an algorithm expressing intersection numbers $<{\tau }_{n,m}{\prod }_{i=0}^{r-1}{\tau }_{0,i}^{k_i}{>}_g$ via correlation functions of primaries.

38 pages

References in corpus (11)

• Hurwitz numbers and intersections on moduli spaces of curves
• Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
• Topological recursion relations in genus 2
• A descendent relation in genus 2
• Hodge integrals and Hurwitz numbers via virtual localization
• Topological recursive relations in $H^{2g}(M_{g,n})$
• Moduli Spaces of Higher Spin Curves and Integrable Hierarchies
• Compactifying the space of stable maps
• A geometric construction of Getzler's relation
• Witten solution of the Gelfand-Dikii hierarchy
• Counting Meromorphic Functions with Critical Points of Large Multiplicities

Cited by in corpus (19)

• Tautological relations and the r-spin Witten conjecture
• An algebro-geometric proof of Witten's conjecture
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• Virasoro constraints for Kontsevich-Hurwitz partition function
• On double Hurwitz numbers in genus 0
• Intersection theory from duality and replica
• A Genus-3 Topological Recursion Relation
• Intersection numbers of Riemann surfaces from Gaussian matrix models
• Intersection numbers with Witten's top Chern class
• A new proof of Faber's intersection number conjecture
• Solution of W-Constraints for R-Spin Intersection Numbers
• Descendent integrals and tautological rings of moduli spaces of curves
• Quantum Deformation Theory of the Airy Curve and Mirror Symmetry of a Point
• From $r$-Spin Intersection Numbers to Hodge Integrals
• Formal pseudodifferential operators and Witten's r-spin numbers
• Buryak-Okounkov formula for the $n$-point function and a new proof of the Witten conjecture
• Combinatorics of binomial decompositions of the simplest Hodge integrals
• Simple Lie algebras and topological ODEs
• Intersections in genus 3 and the Boussinesq hierarchy