On the extension theorem of Hwang and Mok

Abstract

Abstract Jun-Muk Hwang and Ngaiming Mok developed a framework for studying complex Fano (more generally, uniruled) manifolds in terms of their intrinsic local differential-geometric structure: the varieties of minimal rational tangents (VMRT). In particular, their ‘Cartan–Fubini’ extension theorem shows that a Fano manifold of Picard number 1 (satisfying certain technical conditions) is determined, up to biholomorphism, by an analytic germ of its VMRT at a general point. We prove a characteristic-free analogue of this result, replacing the VMRT with families of formal arcs.