The Witten equation and its virtual fundamental cycle

Details The Witten equation and its virtual fundamental cycle The Witten equation and its virtual fundamental cycle

2007-12-24

arxiv.org/abs/0712.4025v3

Mathematics

Algebraic Geometry

Major revision. Additional axioms proved and additional details provided over previous version

Scientific paper

We study a system of nonlinear elliptic PDEs associated with a quasi-homogeneous polynomial. These equations were proposed by Witten as the replacement for the Cauchy-Riemann equation in the singularity (Landau-Ginzburg) setting. We introduce a perturbation to the equation and construct a virtual cycle for the moduli space of its solutions. Then, we study the wall-crossing of the deformation of the virtual cycle under perturbation and match it to classical Picard-Lefschetz theory. An extended virtual cycle is obtained for the original equation. Finally, we prove that the extended virtual cycle satisfies a set of axioms similar to those of Gromov-Witten theory and r-spin theory.

Affiliated with

Also associated with

No associations

Rating

The Witten equation and its virtual fundamental cycle 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 and its virtual fundamental cycle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Witten equation and its virtual fundamental cycle will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-184599