Cohomologie quantique orbifolde des espaces projectifs a poids

2005/10/16 by Étienne Mann, Mann, Etienne · 4 citations
Mathematics · #14N35 #32S20 #32S30 #53D45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.math/0510331

openalex publication_date 2005/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2001, S. Barannikov showed that the Frobenius manifold coming from the quantum cohomology of the complex projective space is isomorphic to the Frobenius manifold attached to some Laurent polynomial. The purpose of this thesis is to generalize this result. More precisely, we show, up to a conjecture on the value of some orbifold Gromov-Witten invariants, that the Frobenius structure obtained on the orbifold quantum cohomology of the weighted projective spaces is isomorphic to the one attached to some Laurent polynomial.

Cited by

• Mixed Hodge structures for vanishing cycles and orbifold cohomology
• Crepant resolutions of weighted projective spaces and quantum deformations
• On Bott's residue formula for toric complete intersections
• On the algebraic hypersurfaces invariant by weighted projective foliations

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• Orbifold quantum cohomology of weighted projective spaces
• Gromov-Witten theory of orbicurves, the space of tri-polynomials and Symplectic Field Theory of Seifert fibrations
• The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits
• Orbifold Quantum Cohomology
• Three constructions of Frobenius manifolds: a comparative study