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

2019/11/01 by Alexis Roquefeuil, Roquefeuil, Alexis
Mathematics · #14N35 (Primary) #39A45 #53D45 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1911.00243

openalex publication_date 2019/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Givental's K-theoretical J-function can be used to reconstruct genus zero\nK-theoretical Gromov--Witten invariants. We view this function as a\nfundamental solution of a q-difference system. In the case of projective\nspaces, we show that we can use the confluence of q-difference systems to\nobtain the cohomological J-function from its K-theoretic analogue. This\nprovides another point of view to one of the statements of Givental--Tonita's\nquantum Hirzebruch--Riemann--Roch theorem. Furthermore, we compute connection\nnumbers in the equivariant setting.\n

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