Daniel Huybrechts (University of Bonn)
Résultats de finitude en géométrie algébrique (notamment pour des surfaces K3 et des variétés hyperkählériennes)
In the moduli space of polarized varieties the same unpolarized variety can occur multiple times However, for K3 surfaces, compact hyperkähler manifolds, and abelian varieties the number is finite. This may be viewed as a consequence of the Kawamata-Morrison cone conjecture. We explain how to prove this finiteness without using the cone conjecture. Instead, we use the geometry of the moduli space of polarized varieties to conclude the finiteness by means of Baily-Borel type arguments. We also address related questions concerning finiteness in twistor families associated with polarized K3 surfaces of CM type.