The local/logarithmic correspondence and the degeneration formula for quasimaps
Algebraic Geometry
2026-01-14 v1
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 arXiv:1712.05210 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.
Keywords
Cite
@article{arxiv.2404.01381,
title = {The local/logarithmic correspondence and the degeneration formula for quasimaps},
author = {Alberto Cobos Rabano and Cristina Manolache and Qaasim Shafi},
journal= {arXiv preprint arXiv:2404.01381},
year = {2026}
}
Comments
37 pages, 4 figures, comments welcome