On the equidistribution of totally geodesic submanifolds in compact locally symmetric spaces and application to boundedness results for negative curves and exceptional divisors

Vincent Koziarz (1) , Julien Maubon (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 IECL - Institut Élie Cartan de Lorraine

We prove an equidistribution result for totally geodesic submanifolds in a compact locally symmetric space. In the case of Hermitian locally symmetric spaces, this gives a convergence theorem for currents of integration along totally geodesic subvarieties. As a corollary, we obtain that on a 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, we prove that 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.

Domaines: Géométrie différentielle [math.DG]; Géométrie algébrique [math.AG]

Vincent Koziarz, Julien Maubon. On the equidistribution of totally geodesic submanifolds in compact locally symmetric spaces and application to boundedness results for negative curves and exceptional divisors. 2015. ⟨hal-01266101⟩