Universal covers and the GW/Kronecker correspondence
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).
Keywords
Cite
@article{arxiv.1011.4897,
title = {Universal covers and the GW/Kronecker correspondence},
author = {Jacopo Stoppa},
journal= {arXiv preprint arXiv:1011.4897},
year = {2011}
}
Comments
33 pages, 8 figures. Completely revised, published version