On the invariance of Welschinger invariants (Erwan Brugallé, Université de Nantes)

25.02.2019 16:00

Welshinger invariants are real analogs of Gromov-Witten invariants for symplectic 4-manifolds X. In this talk, I will strengthen the original Welschinger's invariance result.
Our main result is that when X is a real rational algebraic surface, Welschinger invariants eventually only depend on the number of real interpolated points, and some homological data associated to X.
This result follows easily from a formula relating Welschinger invariants of two real symplectic manifolds differing by a surgery along a real Lagrangian sphere. As an application, we complete the computation of Welschinger invariants of real rational algebraic surfaces, and obtain vanishing, sign, and sharpness results generalizing previously known statements. If time permits, we will also discuss some hypothetical relations with tropical refined invariants defined by Block-Göttsche and Göttsche-Schroeter.

Lieu

Bâtiment: Battelle

Séminaire "Fables géométriques "

entrée libre