Selected Publications
- E. Rousseau :Equations diff ´ erentielles sur les hypersurfaces de P4, J. Math. Pures Appl. (9) 86 (2006), no. 4, 322–341.
- G. Pacienza, E. Rousseau : On the logarithmic Kobayashi conjecture, J. Reine Angew. Math. 611 (2007), 221–235.
- S. Diverio, J. Merker, E. Rousseau : Effective algebraic degeneracy, Invent. Math. 180 (2010), no. 1, 161-223.
- X. Roulleau, E. Rousseau : Canonical surfaces with big cotangent bundle, Duke Math. J. 163 (2014), no.7, 1337–1351.
- E. Rousseau : Hyperbolicity, automorphic forms and Siegel modular varieties, Ann. Sci Ec. Norm. Super. (4) 49 (2016), no. 1, 249–255.
FRIAS Project
On hyperbolicity in complex geometry
This project is concerned with pure mathematics, more specifically complex geometry and its conjectural interactions with arithmetic on the existence of solutions of polynomial equations. The importance of these questions is illustrated by Faltings’s proof of the Mordell conjecture on the finiteness of rational points on algebraic curves of genus greater than 1. The project is based on questions in complex geometry whose solution resides in positivity properties of certain geometric structures. This positivity is most often expressed in geometric consequences (on entire curves) and arithmetic (on rational points).
Three directions can be seen to structure this project:
Singular varieties: we plan to investigate hyperbolic properties of singular varieties such as singular quotients of bounded symmetric domains.
Holomorphic foliations: we study how the positivity of the canonical bundle impacts the existence on projective varieties of entire curves tangent to foliations.
Orbifold structures: the success of the minimal model program and recent works of Campana and Miyaoka show that the use in hyperbolicity of the logarithmic pairs of birational geometry is promising.