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A complex submanifold in a complex manifold satisfies the formal principle if its formal neighborhood determines its biholomorphic germ. A smooth rational curve in a complex manifold satisfies the formal principle if its normal bundle is positive. It is unknown whether a rational curve with semi-positive normal bundle satisfies the formal principle. We discuss the simplest unknown case of a smooth rational curve in a threefold whose normal bundle is the direct sum of a trivial line bundle and a line bundle of degree 1. [-]
A complex submanifold in a complex manifold satisfies the formal principle if its formal neighborhood determines its biholomorphic germ. A smooth rational curve in a complex manifold satisfies the formal principle if its normal bundle is positive. It is unknown whether a rational curve with semi-positive normal bundle satisfies the formal principle. We discuss the simplest unknown case of a smooth rational curve in a threefold whose normal ...[+]

32K07 ; 58A15 ; 32C22

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