BRANE ACTIONS, CATEGORIFICATION OF GROMOV-WITTENTHEORY AND QUANTUM K-THEORY

Abstract : Let X be a smooth projective variety. Using the idea of brane actions discovered by Toën, we construct a lax associative action of the operad of stable curves of genus zero on the variety X seen as an object in correspondences in derived stacks. This action encodes the Gromov-Witten theory of X in purely geometrical terms and induces an action on the derived category Qcoh(X) which allows us to recover the formulas for Quantum K-theory of Givental-Lee. This paper is the first step of a larger project. We believe that this action in correspondences encodes the full classical cohomological Gromov-Witten invariants of X. This will appear in a second paper.
Type de document :
Article dans une revue
Geometry and Topology, Mathematical Sciences Publishers, In press
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01151061
Contributeur : Etienne Mann <>
Soumis le : vendredi 1 décembre 2017 - 09:58:58
Dernière modification le : vendredi 16 novembre 2018 - 02:14:49

Fichier

finalversionGT-GW.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01151061, version 2

Citation

Etienne Mann, Marco Robalo. BRANE ACTIONS, CATEGORIFICATION OF GROMOV-WITTENTHEORY AND QUANTUM K-THEORY. Geometry and Topology, Mathematical Sciences Publishers, In press. 〈hal-01151061v2〉

Partager

Métriques

Consultations de la notice

149

Téléchargements de fichiers

50