GROMOV-WITTEN THEORY WITH DERIVED ALGEBRAIC GEOMETRY

Etienne Mann (1) , Marco Robalo (2)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

In this survey we add two new results that are not in our paper [MR15]. 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 a smooth variety X seen as an object in correspondences in derived stacks. This action encodes the Gromov-Witten theory of X in purely geometrical terms.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Etienne Mann, Marco Robalo. GROMOV-WITTEN THEORY WITH DERIVED ALGEBRAIC GEOMETRY. Panoramas et synthèses, 2021, 55, pp.147-186. ⟨hal-01739898⟩