2022/04/21 by Hwang, Jun-Muk
#14L30 #32J05 #58A30 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2204.09927
We study minimal rational curves on a complex manifold that are tangent to a distribution. In this setting, the variety of minimal rational tangents (VMRT) has to be isotropic with respect to the Levi tensor of the distribution. Our main result is a converse of this: any smooth projective variety isotropic with respect to a vector-valued anti-symmetric form can be realized as VMRT of minimal rational curves tangent to a distribution on a complex manifold. The complex manifold is constructed as a partial equivariant compactification of a metabelian group, which is a result of independent interest.