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arXiv · 1011.4897

Universal covers and the GW/Kronecker correspondence

Jacopo Stoppa
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Abstract

The tropical vertex is an incarnation of mirror symmetry found by Gross, Pandharipande and Siebert. It can be applied to m-Kronecker quivers K(m) (together with a result of Reineke) to compute the Euler characteristics of the moduli spaces of their (framed) representations in terms of Gromov-Witten invariants (as shown by Gross and Pandharipande). In this paper, we study a possible geometric picture behind this correspondence, in particular constructing rational tropical curves from subquivers of the universal covering quiver of K(m). Additional motivation comes from the physical interpretation of m-Kronecker quivers in the context of quiver quantum mechanics (especially work of F. Denef).

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Jacopo Stoppa. 2010-11-22. Universal covers and the GW/Kronecker correspondence. https://arxiv.org/abs/1011.4897

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