Séminaire de Géométrie Tropicale

Institut Mathématiques de Jussieu ,
Université Pierre et Marie Curie, Paris 6
UMR CNRS 7586

Centre de Mathématiques Laurent Schwartz ,
École Polytechnique
UMR CNRS 7640



Mercredi 28 septembre, 14h salle 1525-502



Eugenii Shustin (Tel Aviv University)

On refined tropical invariants of toric surfaces

Résumé : We discuss two examples of refined count of plane tropical curves. One of them is the refined broccoli invariant. It was introduce by Goettsche and Schroeter for genus zero case, and it turns into some descendant invariant or the broccoli invariant according as the parameter takes value 1 or -1. A possible extension of broccoli invariant to positive genera appeared to be rather problematic. However, the refined version turns to be easier to treat. Jointly with F. Schroeter, we have defined a refined broccoli invariant, counting elliptic tropical curves. This can be done for higher genera as well (work in progress). Another example (joint work with L. Blechman) is the refined descendant tropical invariant (involving arbitrary powers of psi-classes). We discuss also the complex and real enumerative meaning of these invariants.