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Gromov-Witten theory of bicyclic pairs

Author:
Michel van Garrel, Navid Nabijou, Yannik Schuler
Keyword:
Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)
journal:
--
date:
2023-10-08 16:00:00
Abstract
A bicyclic pair is a smooth surface equipped with a pair of smooth divisors intersecting in two reduced points. Resolutions of self-nodal curves constitute an important special case. We investigate the logarithmic Gromov-Witten theory of bicyclic pairs. We establish all-genus correspondences with local Gromov-Witten theory and open Gromov-Witten theory, and a genus zero correspondence with orbifold Gromov-Witten theory. For self-nodal curves in $\mathbb{P}(1,1,r)$ we obtain a closed formula for the genus zero invariants and relate these to the invariants of local curves. We also establish a conceptual relationship to the invariants obtained by smoothing the self-nodal curve. The technical heart of the paper is a qualitatively new analysis of the degeneration formula for stable logarithmic maps, complemented by torus localisation and scattering techniques.
PDF: Gromov-Witten theory of bicyclic pairs.pdf
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