Work

A mirror theorem for non-split toric bundles

Year: 2025

Type: article

Abstract: We construct an I -function for toric bundles obtained as a fiberwise GIT quotient of a (not necessarily split) vector bundle. This is a generalization of Brown’s I -function for split toric bundles (Brown in Int Math Res Not IMRN 19:5437–5482, 2014) and the I -function for non-split projective bundles (Iritani and Koto in arXiv:2307.03696 [math.AG], 2023). In order to prove the mirror theorem, we establish a characterization of points on the Givental Lagrangian cones of toric bundles and prove a mirror theorem for the twisted Gromov–Witten theory of a fiber product of projective bundles. The former result generalizes Brown’s characterization for split toric bundles [6] to the non-split case.

Source: Mathematische Annalen

DOI: 10.1007/s00208-025-03302-7

Author: Yuki Koto

Institutions: Institute of Mathematics, Academia Sinica, Academia Sinica

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Academia Sinica, Japan Society for the Promotion of Science