Deformation rigidity of the rational homogeneous space associated to a long simple root
By Jun-Muk Hwang, N. Mok. 2002
54 citations recorded by the source corpus.
Abstract As a continuation of our previous works we study the conjecture on the rigidity under Kahler deformation of the complex structure of rational homogeneous spaces G/P of Picard number 1, confirming its validity whenever G/P is associated to a long simple root. For these rational homogeneous spaces the minimal G-invariant holomorphic distribution D is spanned by varieties of minimal rational tangents, and, excepting the symmetric and the contact cases, the complex structure of G/P is completely determined by the nilpotent symbol algebra of the weak derived differential system of D. The problem is reduced, in a sense, to the invariance of this nilpotent symbol algebra under Kahler deformation. In our earlier works in relation to the question of the integrability of distributions spanned by varieties of minimal rational tangents we have established identities on Lie brackets using integral surfaces arising from pencils of rational curves. In the case on hand, at a point o∈G/P we prove that the nilpotent symbol algebra at o is nothing other than the universal Lie algebra generated by Do subject to these identities on Lie brackets, by verifying that they correspond to finiteness condition in the Serre presentation of the simple Lie algebra G.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5ee0e035e3705d07d80a9dbb64899ba6f7edd1d4
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Rigidity of rational homogeneous spaces (2006, background): “1 when b2(S) = 1 has been proved in a series of works [10], [13] [16], [17], [19].”