Gromov-Witten theory of orbicurves, the space of tri-polynomials and Symplectic Field Theory of Seifert fibrations

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dc.creatorRossi, Paolo
dc.date2008-08-19
dc.date2008-09-18
dc.date.accessioned2026-07-07T10:03:25Z
dc.date.available2026-07-07T10:03:25Z
dc.descriptionWe compute, with Symplectic Field Theory techniques, the Gromov-Witten theory of the complex projective line with orbifold points. A natural subclass of these orbifolds, the ones with polynomial quantum cohomology, gives rise to a family of (polynomial) Frobenius manifolds and integrable systems of Hamiltonian PDEs, which extend the (dispersionless) bigraded Toda hierarchy. We then define a Frobenius structure on the spaces of polynomials in three complex variables of the form F(x,y,z)= -xyz+P_1(x)+P_2(y)+P_3(z) which contains as special cases the ones constructed on the space of Laurent polynomials. We prove a mirror theorem stating that these Frobenius structures are isomorphic to the ones found before for polynomial P1-orbifolds. Finally we link rational Symplectic Field Theory of Seifert fibrations over S^2 and three singular fibers with orbifold Gromov-Witten invariants of the base, extending a known result valid in the smooth case.
dc.description(fixed a mistake in computing flat coordinates for tri-polynomials)
dc.identifierhttps://arxiv.org/abs/0808.2626
dc.identifierhttp://arxiv.org/abs/0808.2626
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169281
dc.subjectSymplectic Geometry
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.titleGromov-Witten theory of orbicurves, the space of tri-polynomials and Symplectic Field Theory of Seifert fibrations
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