On refined tropical invariants of toric surfaces (Eugenii Shustin, School of Mathematical Sciences at the Tel-Aviv University)

09.05.2016 18:30 – 19:15

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 most interesting related question: What is the complex and real enumerative meaning of these invariants?

Lieu

Bâtiment: Battelle

Villa Battelle, Séminaire "Fables géométriques"

entrée libre