THE LOCAL/LOGARITHMIC CORRESPONDENCE AND THE DEGENERATION FORMULA FOR QUASIMAPS
Abstract
Abstract We study the relationship between the enumerative geometry of rational curves in local geometries and various versions of maximal contact logarithmic curve counts. Our approach is via quasimap theory, and we show versions of the [vGGR19] local/logarithmic correspondence for quasimaps, and in particular for normal crossings settings, where the Gromov-Witten theoretic formulation of the correspondence fails. The results suggest a link between different formulations of relative Gromov-Witten theory for simple normal crossings divisors via the mirror map. The main results follow from a rank reduction strategy, together with a new degeneration formula for quasimaps.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Algebra and Logic
Rings
Modules
and Algebras
Publication details
- Journal / source
- Journal of the Institute of Mathematics of Jussieu
- Publisher
- Cambridge University Press (CUP)
- Volume
- 25
- Issue
- 2
- Pages
- 1237–1280
- Publication date
- 13 January 2026
- Language
- EN