2007/09/18 by Paolo Rossi
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Class (philosophy) #Cohomology #Differential geometry #Field (mathematics) #Geometry and complex manifolds #Gromov–Witten invariant #KdV hierarchy #Korteweg–de Vries equation #Mathematics #Physics #Pure mathematics #Quantization (signal processing) #Quantum cohomology #Quantum mechanics #Riemann surface #Symplectic geometry #Symplectic manifold #Symplectic representation #math-ph #math.MP #math.SG
paper · pdf · doi:10.1016/j.geomphys.2008.02.012
published as J.Geom.Phys.58:931-941,2008 · 13 pages
arxiv created 2007/09/18 · openalex publication_date 2008/03/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We compute the Gromov-Witten potential at all genera of target smooth Riemann surfaces using Symplectic Field Theory techniques and establish differential equations for the full descendant potential. This amounts to impose (and possibly solve) different kinds of Schroedinger equations related to some quantization of the dispersionless KdV hierarchy. In particular we find very explicit formulas for the Gromov-Witten invariants of low degree of P1 with descendants of the Kaehler class.