Hyperbolicity in Complex Geometry

By Y. Siu. 2004

93 citations recorded by the source corpus.

How researchers see this paper

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Holomorphic Morse Inequalities and the Green-Griffiths-Lang Conjecture (2010, methodology): “This strategy first devised by [Siu02, Siu04] has indeed been successful in some cases for the study of generic algebraic degeneracy (e.g. for hypersurfaces of very large degree in Pn+1C ).”
Recent results on the Kobayashi and Green-Griffiths-Lang conjectures (2018, methodology): “The following result strengthens the initial announcement of [Siu04].”
Vector fields on the total space of hypersurfaces in the projective space and hyperbolicity (2008, methodology): “Siu’s approach [18], we have shown that the image of φ is contained in an algebraic curve.”
On the hyperbolicity of general hypersurfaces (2016, methodology): “In [56], Siu generalized Voisin’s variational method from [59] to higher order jet spaces, and outlined a strategy to prove Kobayashi’s conjecture.”
Hyperbolicity of generic high-degree hypersurfaces in complex projective space (2012, methodology): “1 was presented with a sketch of its proof in [22] and [23].”
Low pole order frames on vertical jets of the universal hypersurface (2008, methodology): “They are called vertical jets in [18, 13, 16] and will be denoted by J vert (X0).”