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Formal principle for rational curves in complex threefolds

By Jun-Muk Hwang

Appears in collection : Complex Geometry, Dynamical Systems and Foliation Theory / Géométrie complexe, systèmes dynamiques et théorie de feuilletages

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.

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Citation data

  • DOI 10.24350/CIRM.V.19969503
  • Cite this video Hwang Jun-Muk (10/20/22). Formal principle for rational curves in complex threefolds. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19969503
  • URL https://dx.doi.org/10.24350/CIRM.V.19969503

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