Скачать или смотреть Jun Muk Hwang: On Hirschowitz's conjecture on the formal principle

A conjecture of Hirschowitz's predicts that a compact complex submanifold in a complex manifold satisfies the formal principle, namely, its formal neighborhood determines the germ of its Euclidean neighborhoods up to biholomorphisms, if the submanifold has unobstructued deformation and its normal bundle is globally generated. By applying Cartan's equivalence method to a suitable differential system on the universal family of the deformation space of the complex submanifold, I have proved the conjecture for a general deformation of the submanifold under the additional assumption that the sections of the normal bundle separate points. As corollaries, we see that a sufficiently general smooth free rational curve on a complex manifold satisfies the formal principle and also the zero section of a globally generated vector bundle on a Fano manifold satisfies the formal principle.