The Abelian/Nonabelian Correspondence and Gromov–Witten Invariants of Blow-Ups. (24th August 2022)

• Record Type: Journal Article
• Authors: Coates, Tom; Lutz, Wendelin; Shafi, Qaasim
• Is Part Of: Forum of mathematics. Volume 10(2022)
• Publication Date: 2022-08-24
• Subjects: 14N35; Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2022.46
• Languages: English
• ISSNs: 2050-5094

Abstract

Abstract: We prove the abelian/nonabelian correspondence with bundles for target spaces that are partial flag bundles, combining and generalising results by Ciocan-Fontanine–Kim–Sabbah, Brown, and Oh. From this, we deduce how genus-zero Gromov–Witten invariants change when a smooth projective variety X is blown up in a complete intersection defined by convex line bundles. In the case where the blow-up is Fano, our result gives closed-form expressions for certain genus-zero invariants of the blow-up in terms of invariants of X . We also give a reformulation of the abelian/nonabelian Correspondence in terms of Givental's formalism, which may be of independent interest.