The University of Michigan Combinatorics Seminar
Fall 2009
October 2, 4:10-5:00, 3866 East Hall



Tropical Welschinger invariants

Ilia Itenberg

IRMA, Université de Strasbourg


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 (piecewise-linear objects which can be seen as algebraic curves over the tropical semifield).

We define a series of tropical Welschinger-type invariants of the projective plane. These invariants can be seen as real tropical analogs of relative Gromov-Witten 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.