Finiteness of totally geodesic exceptional divisors in Hermitian locally symmetric spaces
Language
en
Article de revue
This item was published in
Bulletin de la société mathématique de France. 2018, vol. 146, n° 4, p. 613-631
Société Mathématique de France
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Bounded Negativity conjecture
Hermitian locally symmetric spaces
totally geodesic submanifold
equidistribution
negative curve
exceptional divisor
current of integration
Origin
Hal imported