Séminaire de Géométrie Tropicale
09 Novembre 2011, 16h15 salle 1516-413
Résumé :
Refining Node Polynomials for Plane Curves
According to the Goettsche Conjecture (now a theorem), the
degree of the Severi variety of plane curves of degree d with delta
nodes is given by a (node) polynomial N_delta(d) in d, provided d is
large enough. Recently, Goettsche and Shende conjectured the existence
of "refined" node polynomials N_delta(d; y), which specialize at y = 1
to N_delta(d), and at y = -1 to Welschinger numbers of the complex
projective plane.
In this talk, I discuss a construction of such polynomials using
tropical geometry and some of their properties.