A Caporaso-Harris type Formula for relative refined invariants

Abstract

G. Mikhalkin introduced a refined count for real rational curves in a toric surface which pass through some points on the toric boundary of the surface. The refinement is provided by the value of a so-called quantum index. Moreover, he proved that the result of this refined count does not depend on the choice of the points. The correspondence theorem allows one to compute these invariants using the tropical geometry approach and the refined Block-Göttsche multiplicities. In this paper we give a recursive formula for these invariants, that leads to an algorithm to compute them.

26 pages

References in corpus (2)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Patchworking singular algebraic curves, non-Archimedean amoebas and enumerative geometry

Cited by in corpus (1)

• A Tropical Computation of Refined Toric Invariants