Cohomologie quantique orbifolde des espaces projectifs a poids

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.

arXiv comment136 pages in French, 4 figures, PhD thesis at IRMA Strasbourg

References in corpus (1)

• Semi-infinite Hodge structures and mirror symmetry for projective spaces

Cited by in corpus (10)

• A Bott type residue formula on complex orbifolds
• The Quantum Orbifold Cohomology of Weighted Projective Spaces
• Crepant resolutions of weighted projective spaces and quantum deformations
• Quantum cohomology of the Grassmannian and alternate Thom-Sebastiani
• Residue formula for Morita-Futaki-Bott invariant on orbifolds
• Some examples of non-massive Frobenius manifolds in Singularity Theory
• On the Poincaré problem for foliations on compact toric orbifolds
• On the algebraic hypersurfaces invariant by weighted projective foliations
• From Hodge theory for tame functions to Ehrhart theory for polytopes
• A reconstruction theorem for genus zero Gromov-Witten invariants of stacks