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arXiv · 2409.09472

Correlated Gromov-Witten Invariants

Thomas Blomme·Francesca Carocci
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Abstract

We introduce a geometric refinement of Gromov-Witten invariants for $\mathbb P^1$-bundles relative to the natural fiberwise boundary structure. We call these refined invariant correlated Gromov-Witten invariants. Furthermore, we prove a refinement of the degeneration formula keeping track of the correlation. Finally, combining certain invariance properties of the correlated invariant, a local computation and the refined degeneration formula we follow floor diagram techniques to prove regularity results for the generating series of the invariants in the case of $\mathbb P^1$-bundles over elliptic curves. Such invariants are expected to play a role in the degeneration formula for reduced Gromov-Witten invariants for abelian and K3 surfaces.

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Thomas Blomme, Francesca Carocci. 2024-09-14. Correlated Gromov-Witten Invariants. https://doi.org/10.3842/sigma.2025.046

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