Orbifold quantum cohomology of weighted projective spaces

Etienne Mann (1, 2, 3)

1 IRMA - Institut de Recherche Mathématique Avancée
2 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
3 I3M - Institut de Mathématiques et de Modélisation de Montpellier

This article is a revised, short and english version of my PhD thesis. First, we show a mirror theorem : the Frobenius manifold associated to the orbifold quantum cohomology of weighted projective space is isomorphic to the one attached to a specific Laurent polynomial. Secondly, we show a reconstruction theorem, that is, we can reconstruct in an algorithmic way the full genus 0 Gromov-Witten potential from the 3-point invariants.

Mots clés: Quantum cohomology; Gromov-Witten invariant; Frobenius manifold; singularity theory; mirror symmetry

Domaines: Géométrie algébrique [math.AG]; Géométrie symplectique [math.SG]

Etienne Mann. Orbifold quantum cohomology of weighted projective spaces. Journal of Algebraic Geometry, 2008, 17 (1), http://www.ams.org/distribution/jag/2008-17-01/S1056-3911-07-00465-1/home.html. ⟨10.1090/S1056-3911-07-00465-1⟩. ⟨hal-00124722⟩