Séminaire de géométrie - Salle de conférences du CMLS - 10h

10h-11h – Luis Gustavo Mendes (Universidade Federal do Rio Grande do Sul, Brasil) :

"Birational geometry of special quotient foliations and Chazy's equations"

Abstract : The works of Brunella and Santos have singled out three special singular holomorphic foliations on projective surfaces having invariant rational
nodal curves of positive self-intersection.

These foliations can be described as quotients of foliations on  rational surfaces under cyclic groups of transformations of orders three, four, and six, respectively.

Through an unexpected connection with the reduced Chazy IV, V and VI equations, we give explicit models for the  three foliations as quadratic foliations on the projective plane.

We describe the full groups of birational automorphisms of these quotient foliations and different realizations as Cremona transformations, and, through this, we produce symmetries for the reduced Chazy IV and V equations.

Joint work with Adolfo Guillot.