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.

v1: 15 pages. v2: 26 pages, 8 figures. Added several sections including a discussion of relation to refined Severi degrees

References in corpus (3)

• Refined curve counting with tropical geometry
• Refined curve counting on complex surfaces
• Abelian quiver invariants and marginal wall-crossing

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