The Spin Gromov-Witten/Hurwitz correspondence for $\mathbb{P}^1$ - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

The Spin Gromov-Witten/Hurwitz correspondence for $\mathbb{P}^1$

Résumé

We study the spin Gromov-Witten (GW) theory of $\mathbb{P}^1$. Using the standard torus action on $\mathbb{P}^1$, we prove that the associated equivariant potential can be expressed by means of operator formalism and satisfies the 2-BKP hierarchy. As a consequence of this result, we prove the spin analogue of the GW/Hurwitz correspondence of Okounkov-Pandharipande for $\mathbb{P}^1$, which was conjectured by J. Lee. Finally, we prove that this correspondence for a general target spin curve follows from a conjectural degeneration formula for spin GW invariants that holds in virtual dimension 0.

Dates et versions

hal-03835410 , version 1 (31-10-2022)

Identifiants

Citer

Alessandro Giacchetto, Reinier Kramer, Danilo Lewański, Adrien Sauvaget. The Spin Gromov-Witten/Hurwitz correspondence for $\mathbb{P}^1$. 2022. ⟨hal-03835410⟩
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