The Toda equations and the Gromov-Witten theory of the Riemann sphere

Details The Toda equations and the Gromov-Witten theory of the Riemann sphere The Toda equations and the Gromov-Witten theory of the Riemann sphere

1999-12-20

arxiv.org/abs/math/9912166v1

Mathematics

Algebraic Geometry

16 pages, LaTeX2e

Scientific paper

Consequences of the Toda equations arising from the conjectural matrix model for the Riemann sphere are investigated. The Toda equations determine the Gromov-Witten descendent potential (including all genera) of the Riemann sphere from the degree 0 part. Degree 0 series computations via Hodge integrals then lead to higher degree predictions by the Toda equations. First, closed series forms for all 1-point invariants of all genera and degrees are given. Second, degree 1 invariants are investigated with new applications to Hodge integrals. Third, a differential equation for the generating function of the classical simple Hurwitz numbers (in all genera and degrees) is found -- the first such equation. All these results depend upon the conjectural Toda equations. Finally, proofs of the Toda equations in genus 0 and 1 are given.

Affiliated with

Also associated with

No associations

Rating

The Toda equations and the Gromov-Witten theory of the Riemann sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Toda equations and the Gromov-Witten theory of the Riemann sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Toda equations and the Gromov-Witten theory of the Riemann sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-44485