Brane actions, categorifications of Gromov–Witten theory and quantum K–theory

Mann, Etienne¹ ; Robalo, Marco²

¹ LAREMA UMR - 6093, Département de Mathématiques Bâtiment I, Faculté des Sciences 2, Université d’Angers, Angers, France
² Sorbonne Université, Faculté des Sciences et Ingénierie, Institut de Mathématiques de Jussieu-PRG, Paris, France

Geometry & topology, Tome 22 (2018) no. 3, pp. 1759-1836.

Résumé

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 $Qcoh\left(X\right)$ which allows us to recover the quantum K–theory of Givental and Lee.

Détail

DOI : 10.2140/gt.2018.22.1759

Classification : 14N35
Keywords: Gromov–Witten theory, higher category, derived algebraic geometry

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