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Conference Paper: Geometric substructures and uniruled projective subvarieties of Fano manifolds of Picard number 1
Title | Geometric substructures and uniruled projective subvarieties of Fano manifolds of Picard number 1 |
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Authors | |
Issue Date | 2016 |
Citation | The Pacific Rim Conference on Complex & Symplectic Geometry XI, University of Science and Technology of China, Hefei, Anhui, China, 26 July - 1 August 2016 How to Cite? |
Abstract | In the late 1990s Hwang and Mok initiated a geometric theory of uniruled projective manifolds modeled on their varieties of minimal rational tangents (VMRTs), proving later on Cartan-Fubini extension (2001), according to which a germ of VMRT-preserving biholomorphism f : (X; x0) → (Y ; y0) between two Fano manifolds of Picard number 1 extends necessarily to a biholomorphism F : X → Y whenever their VMRTs are of positive dimension and Gauss maps on VMRTs are generically finite. Hong-Mok (2010) extended Cartan-Fubini extension to the non-equidimensional setting under a relative nondegeneracy condition on second fundamental forms on VMRTs. Recently Mok-Zhang considered the analytic continuation of a germ of complex submanifold (S; x0) ,→ (X; x0) of a Fano manifold of Picard number 1 uniruled by lines, where S inherits a sub-VMRT structure defined by intersections of VMRTs with tangent spaces. Assuming that sub-VMRTs satisfy new non-degeneracy conditions and that the distribution spanned by sub-VMRTs is bracket-generating, we showed that S ⊂ Z for some irreducible subvariety Z ⊂ X, dim(Z) = dim(S) by constructing a universal family of chains of rational curves by an analytic process and proving its algebraicity. |
Persistent Identifier | http://hdl.handle.net/10722/236911 |
DC Field | Value | Language |
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dc.contributor.author | Mok, N | - |
dc.date.accessioned | 2016-12-15T10:34:35Z | - |
dc.date.available | 2016-12-15T10:34:35Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | The Pacific Rim Conference on Complex & Symplectic Geometry XI, University of Science and Technology of China, Hefei, Anhui, China, 26 July - 1 August 2016 | - |
dc.identifier.uri | http://hdl.handle.net/10722/236911 | - |
dc.description.abstract | In the late 1990s Hwang and Mok initiated a geometric theory of uniruled projective manifolds modeled on their varieties of minimal rational tangents (VMRTs), proving later on Cartan-Fubini extension (2001), according to which a germ of VMRT-preserving biholomorphism f : (X; x0) → (Y ; y0) between two Fano manifolds of Picard number 1 extends necessarily to a biholomorphism F : X → Y whenever their VMRTs are of positive dimension and Gauss maps on VMRTs are generically finite. Hong-Mok (2010) extended Cartan-Fubini extension to the non-equidimensional setting under a relative nondegeneracy condition on second fundamental forms on VMRTs. Recently Mok-Zhang considered the analytic continuation of a germ of complex submanifold (S; x0) ,→ (X; x0) of a Fano manifold of Picard number 1 uniruled by lines, where S inherits a sub-VMRT structure defined by intersections of VMRTs with tangent spaces. Assuming that sub-VMRTs satisfy new non-degeneracy conditions and that the distribution spanned by sub-VMRTs is bracket-generating, we showed that S ⊂ Z for some irreducible subvariety Z ⊂ X, dim(Z) = dim(S) by constructing a universal family of chains of rational curves by an analytic process and proving its algebraicity. | - |
dc.language | eng | - |
dc.relation.ispartof | Pacific Rim Conference on Complex & Symplectic Geometry, 2016 | - |
dc.title | Geometric substructures and uniruled projective subvarieties of Fano manifolds of Picard number 1 | - |
dc.type | Conference_Paper | - |
dc.identifier.email | Mok, N: nmok@hku.hk | - |
dc.identifier.authority | Mok, N=rp00763 | - |
dc.identifier.hkuros | 270724 | - |