Tag: Minseong Kwon

For each rational homogeneous space, the space of lines is now well-understood and can be described in terms of the induced group action. It is natural to consider rational curves of higher degree, and in this talk, we discuss geometry of conics in adjoint varieties, which are rational homogeneous spaces associated to simple Lie algebras. Each adjoint variety is equipped with a hyperplane distribution called the contact distribution, and we show that smooth conics transverse to the contact distribution form a homogeneous symmetric variety if the adjoint variety is of Picard number 1. This enables us to view the Hilbert scheme of conics as a spherical variety, and we compute its colored fan by using the description of the space of lines and the Hilbert-Chow morphism.

TBA

This is a working seminar to introduce the notion of an integrable G-structure and its obstruction class. In the previous two talks, we discussed the definition of the k-th order structure tensor of a G-structure. In the third talk, we will discuss how the structure tensors can be characterized in terms of classical invariants, namely the curvature tensor and the torsion tensor of a given connection. The main reference is the paper ‘The Integrability Problem for G-structures’ (1965) written by Victor Guillemin.

This is a working seminar to introduce the notion of an integrable G-structure and its obstruction class. In the first talk, I discussed the definition of an integrable G-structure and introduced the existence theorem for the structure tensor. In this talk, I will construct the structure tensor of a G-structure, and then prove that the structure tensor is indeed an obstruction class of the integrability which is lying in the Spencer cohomology group. The main reference is the paper ‘The Integrability Problem for G-structures’ (1965) written by Victor Guillemin.