Survey of finiteness results for hyperkähler manifolds
This paper is a survey of finiteness results in hyperkähler geometry. We review some classical theorems by Sullivan, Kollár–Matsusaka, Huybrechts, as well as theorems in the recent literature by Charles, Sawon, and joint results of the author with Verbitsky. We also strengthen a finiteness theorem of the author. These are extended notes of the author’s talk during the closing conference of the Simons Semester at the Banach Center in Będlewo, Poland.