Finiteness of totally geodesic exceptional divisors in Hermitian locally symmetric spaces

Vincent Koziarz

(Joint work with J. Maubon). I will prove that on a smooth complex surface which is a compact quotient of the bidisc or of the 2-ball, there is at most a finite number of totally geodesic curves with negative self intersection. More generally, there are only finitely many exceptional totally geodesic divisors in a compact Hermitian locally symmetric space of the noncompact type of dimension at least 2. This will be deduced from a convergence result for currents of integration along totally geodesic subvarieties in compact Hermitian locally symmetric spaces which itself follows from an equidistribution theorem for totally geodesic submanifolds in a locally symmetric space of finite volume.