Finiteness of totally geodesic exceptional divisors in Hermitian locally symmetric spaces
Langue
en
Article de revue
Ce document a été publié dans
Bulletin de la société mathématique de France. 2018, vol. 146, n° 4, p. 613-631
Société Mathématique de France
Résumé en anglais
We 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 ...Lire la suite >
We 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 noncompact type of dimension at least 2. This is 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.< Réduire
Mots clés en anglais
Bounded Negativity conjecture
Hermitian locally symmetric spaces
totally geodesic submanifold
equidistribution
negative curve
exceptional divisor
current of integration
Origine
Importé de halUnités de recherche