Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Holomorphic sl(2,C)-differential systems on compact Riemann surfaces and curves in compact quotients of SL(2,C)

We explain the framework, the motivations and the strategy behind a result that constructs holomorphic sl(2,C)-differential systems over some Riemann surfaces Σ_g of genus g≥2 such that the image of the associated monodromy homomorphism is some cocompact Kleinian sub-group Γ⊂SL(2,C). As a consequence, there exist holomorphic maps from Σ_g to the quotient SL(2,C)/Γ that do not factor through any elliptic curve. This answers positively a question asked by Huckleberry and Winkelmann, also raised by Ghys. The talk is based on a joint work with Indranil Biswas (Shiv Nadar University, New Delhi), Lynn Heller (BIMSA, Beijing) and Sebastian Heller (BIMSA, Beijing).