Cartan–Fubini type extension of holomorphic maps for Fano manifolds of Picard number 1

By Jun-Muk Hwang, N. Mok. 2001

77 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9f01570ba5a8ff8a7d9653d62a07065e4ceb315b

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In Geometry and Topology

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Citations in the corpus

Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kähler deformation (2005, background): “... E y at y ∈ Vw in the sense of (5.2) is sent to one of the Euler vector fields of G(2, C 2+2a ). Since orbits of the C ∗ -action exp(CE y) are sent to orbits of the Euler vector field, the image of Vw must cover a standard open set of G(2, C 2+2a ). Moreover δ sends open pieces of P -minimal rati”
Base manifolds for fibrations of projective irreducible symplectic manifolds (2007, background): “one hand, the theory of varieties of minimal rational tangents describes a certain geometric structure arising from minimal rational curves at general points of a Fano manifold X with b 2(X) = 1 (cf. [HwMo1], [HwMo2]). This geometric structure has diﬀerential geometric properties reﬂecting special f”
Finite morphisms onto Fano manifolds of Picard number 1 which have rational curves with trivial normal bundles (2003, methodology): “In [ HM1 ], the authors showed that a projective manifold, which can be the image of a rational homogeneous space G=P of Picard number 1 under a holomorphic map, must be either G=P itself or the projective space.”
Ax-Schanuel for Shimura varieties (2017, unknown): “ra cohomology. Observingthat Wx agrees with Cx(S), the variety of minimal rational tangents (VMRT) at x∈ Sconsisting of [α] ∈ PTx(X) tangent to minimal rational curves passing through x∈ X, Hwang-Mok [13] generalized Theorem B to Fano manifolds of Picard number 1, proving analogously the Cartan-Fubi”