Universal covers and the GW/Kronecker correspondence

Details Universal covers and the GW/Kronecker correspondence Universal covers and the GW/Kronecker correspondence

2010-11-22

arxiv.org/abs/1011.4897v2

Mathematics

Algebraic Geometry

33 pages, 8 figures. Completely revised, published version

Scientific paper

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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