Geometric Structures and Substructures on Uniruled Projective Manifolds

Fano manifolds of coindex three admitting nef tangent bundle

“…By [30,Theorem A.1], U y is isomorphic to G/B, where G is a simple linear algebraic group of rank 2 and B is its Borel subgroup. It turns out that W y is G/P for some parabolic subgroup P of G. By the rigidity results on rational homogeneous manifolds [27,Theorem 3.3…”

Rigidity of pairs of rational homogeneous spaces of Picard number $1$ and analytic continuation of geometric substructures on uniruled projective manifolds

“…For a formulation of the "Recognition Problem" for uniruled projective subvarieties, cf. Mok [Mk16].…”

Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1

“…Now, as the main ingredient for the proof of Theorem 1.2, we state the nonequidimensional Cartan-Fubini type extension theorem, which says the rational extension of germs of holomorphic maps respecting varieties of minimal rational tangents. For an introductory exposition on an analytic continuation along minimal rational curves and Cartan-Fubini extension, we refer to Section 2 of Mok [25]. Proposition 2.5 (Theorem 1.1 of Hong-Mok [8]).…”