The Witten equation, mirror symmetry and quantum singularity theory

Details The Witten equation, mirror symmetry and quantum singularity theory The Witten equation, mirror symmetry and quantum singularity theory

2007-12-24

arxiv.org/abs/0712.4021v3

Mathematics

Algebraic Geometry

Includes resolution of the Witten ADE integrable hierarchies conjecture and Witten's ADE self-mirror conjecture. Several corre

Scientific paper

For any quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a corresponding cohomological field theory associated to the singularity. This theory is analogous to Gromov-Witten theory and generalizes the theory of r-spin curves, which corresponds to the simple singularity A_{r-1}. The main results are that we resolve two outstanding conjectures of Witten. The first conjecture is that ADE-singularities are self-dual; and the second conjecture is that the total potential functions of ADE-singularities satisfy corresponding ADE-integrable hierarchies. Other cases of integrable hierarchies are also discussed.

Affiliated with

Also associated with

No associations

Rating

The Witten equation, mirror symmetry and quantum singularity theory 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 Witten equation, mirror symmetry and quantum singularity theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Witten equation, mirror symmetry and quantum singularity theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-184594