The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Geometriae Dedicata Année : 2013

The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits

Résumé

We first describe a canonical mirror partner (B-model) of the small quantum orbifold cohomology of weighted projective spaces (A-model) in the framework of differential equations: we attach to the A-model (resp. B-model) a D-module on the torus and we show that these two D-modules are isomorphic. This makes the A and B-models mirror partners and yields, in this situation, an explicit and finer version of a recent result of Iritani. Then we study, using the theory of the Kashiwara-Malgrange filtration, their degenerations at the origin and we apply our results to the construction of (classical, limit, logarithmic) Frobenius manifolds.
Fichier principal
Vignette du fichier
0909.4063.pdf (479.94 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00473011 , version 1 (16-01-2024)

Identifiants

Citer

Antoine Douai, Etienne Mann. The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits. Geometriae Dedicata, 2013, vol 164, p. 187-226. ⟨10.1007/s10711-012-9768-3⟩. ⟨hal-00473011⟩
107 Consultations
8 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More