Rational curves and MBM classes on hyperkahler manifolds: a survey

Abstract

This paper deals with rational curves and birational contractions on irreducible holomorphically symplectic manifold. We survey some recent results about minimal rational curves, their deformations, extremal rays associated with these curves, and the geometry of the Kähler cone.

25 pages, to appear in the Progress in Math. volume of the Schiermonnikoog conference on rationality (April 2019)