Quivers and curves in higher dimension

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.

38 pages, 3 figures. Final version published in Transactions of the AMS

References in corpus (24)

• Split States, Entropy Enigmas, Holes and Halos
• Quivers with potentials associated to triangulated surfaces
• Infinitely many N=2 SCFT with ADE flavor symmetry
• The tropical vertex
• Cohomology of quiver moduli, functional equations, and integrality of Donaldson-Thomas type invariants
• Quiver Invariants from Intrinsic Higgs States
• Stable logarithmic maps to Deligne--Faltings pairs II
• Vafa-Witten invariants from exceptional collections
• The quantum tropical vertex
• Attractor flow trees, BPS indices and quivers
• The canonical wall structure and intrinsic mirror symmetry
• Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and Mirror Symmetry
• Decomposition of degenerate Gromov-Witten invariants
• Cohomological Donaldson-Thomas theory of a quiver with potential and quantum enveloping algebras
• Scattering diagrams, stability conditions, and coherent sheaves on ${\mathbb{P}}^2$
• Strong positivity for the skein algebras of the $4$-punctured sphere and of the $1$-punctured torus
• MPS degeneration formula for quiver moduli and refined GW/Kronecker correspondence
• Instanton Correction, Wall Crossing And Mirror Symmetry Of Hitchin's Moduli Spaces
• Donaldson-Thomas invariants from tropical disks
• Donaldson-Thomas Transformation of Double Bruhat Cells in Semisimple Lie Groups
• Strong positivity for quantum theta bases of quantum cluster algebras
• BPS Dendroscopy on Local $P^2$
• Fock-Goncharov dual cluster varieties and Gross-Siebert mirrors
• Holomorphic Floer theory and Donaldson-Thomas invariants