The University of Michigan Combinatorics Seminar


Abstract 

Welschinger invariants are designed to bound from below the number of real rational curves which pass through a given real generic collection of points on a real rational surface. In some cases (for example, in the case of the projective plane) these invariants can be calculated using G. Mikhalkin's approach which deals with a corresponding count of tropical curves (piecewiselinear objects which can be seen as algebraic curves over the tropical semifield). We define a series of tropical Welschingertype invariants of the projective plane. These invariants can be seen as real tropical analogs of relative GromovWitten invariants, and are subject to a recursive formula. As application we obtain several results concerning Welschinger invariants. This is joint work with V. Kharlamov and E. Shustin. 