Block-Göttsche invariants from wall-crossing

Abstract

We show how some of the refined tropical counts of Block and Göttsche emerge from the wall-crossing formalism. This leads naturally to a definition of a class of putative q-deformed Gromov-Witten invariants. We prove that this coincides with another natural q-deformation, provided by a result of Reineke and Weist in the context of quiver representations, when the latter is well defined.

arXiv commentv1: 15 pages. v2: 26 pages, 8 figures. Added several sections including a discussion of relation to refined Severi degrees

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• Scattering diagrams, theta functions, and refined tropical curve counts
• Donaldson-Thomas invariants from tropical disks
• A proof of N.Takahashi's conjecture for $({\mathbb{P}}^2,E)$ and a refined sheaves/Gromov-Witten correspondence
• Real Log Curves in Toric Varieties, Tropical Curves, and Log Welschinger Invariants
• Tropical vertex and real enumerative geometry
• Enumerative geometry of surfaces and topological strings