Work

Quantum K -theory of projective spaces and confluence of q -difference equations

Year: 2025

Type: article

Abstract: Givental’s K -theoretical J -function can be used to reconstruct genus zero K -theoretical Gromov–Witten invariants. We view this function as a fundamental solution of a q -difference system. In the case of projective spaces, we show that we can use the confluence of q -difference systems to obtain the cohomological J -function from its K -theoretic analogue. This provides another point of view to one of the statements of Givental–Tonita’s quantum Hirzebruch–Riemann–Roch theorem. Furthermore, we compute connection numbers in the equivariant K -theoretic setting.

Source: Annales de la faculté des sciences de Toulouse Mathématiques

DOI: 10.5802/afst.1831

Author: Alexis Roquefeuil

Institutions: Centre National de la Recherche Scientifique, Laboratoire Angevin de Recherche en Mathématiques, Université d'Angers

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Agence Nationale de la Recherche, Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science

Awards: Categorification in algebraic geometry, Mirror Symmetry and Irregular Singularities coming from Physics, G6803667113, K-theoretic enumerative invariants and q-difference equations