Gauge theoretical Gromov-Witten invariants and virtual fundamental classes

Details Gauge theoretical Gromov-Witten invariants and virtual fundamental classes Gauge theoretical Gromov-Witten invariants and virtual fundamental classes

2003-01-13

arxiv.org/abs/math/0301131v2

Mathematics

Algebraic Geometry

LaTeX, 33 pages. Comments are welcome! Some references were corrected

Scientific paper

This article is an expanded version of talks given by the authors in Oberwolfach, Bochum, and at the Fano Conference in Torino. Some new results (e. g. the material concerning flag varieties, Quot spaces over $\P^1$, and the generalized quiver representations) were included. The main goal is the construction of gauge theoretical Gromov-Witten type invariants of arbitrary genus associated with certain symplectic factorization problems with additional symmetry, and the computation of these invariants in terms of complex geometric objects. The main tool for describing moduli spaces associated with symplectic factorization problems is the "universal Kobayashi-Hitchin correspondence", which gives canonical isomorphisms ${\cal M}^*\to{\cal M}^{\rm st}$ between gauge theoretic moduli spaces of irreducible solutions of certain PDE's and complex geometric moduli spaces of stable framed holomorphic objects. We state a conjecture for the general situation: When the gauge theoretic problem is of Fredholm type, and the data for ${\cal M}^{\rm st}$ are algebraic, then ${\cal M}^{\rm st}$ admits a canonical perfect obstruction theory in the sense of Behrend-Fantechi, and the Kobayashi-Hitchin isomorphism ${\cal M}^*\to{\cal M}^{\rm st}$ identifies the gauge theoretic and the algebraic virtual fundamental classes. The conjecture was checked for the symplectic factorization problems which yield the toric varieties.

Affiliated with

Also associated with

No associations

Rating

Gauge theoretical Gromov-Witten invariants and virtual fundamental classes 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 Gauge theoretical Gromov-Witten invariants and virtual fundamental classes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gauge theoretical Gromov-Witten invariants and virtual fundamental classes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-323631