Quivers and curves in higher dimension

Argüz, Hülya; Bousseau, Pierrick

doi:10.1090/tran/9232

Quivers and curves in higher dimension
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by Hülya Argüz and Pierrick Bousseau;

Trans. Amer. Math. Soc. 378 (2025), 389-420

DOI: https://doi.org/10.1090/tran/9232

Published electronically: September 3, 2024

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Abstract:

We prove a correspondence between Donaldson–Thomas invariants of quivers with potential having trivial attractor invariants and genus zero punctured Gromov–Witten invariants of holomorphic symplectic cluster varieties. The proof relies on the comparison of the stability scattering diagram, describing the wall-crossing behavior of Donaldson–Thomas invariants, with a scattering diagram capturing punctured Gromov–Witten invariants via tropical geometry.

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