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 Denef).
Universal covers and the GW/Kronecker correspondence
STOPPA, JACOPO
2011-01-01
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 Denef).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
