Isotrivial VMRT-structures of complete intersection type

The family of varieties of minimal rational tangents on a quasi-homogeneous projective manifold is isotrivial. Conversely, are projective manifolds with isotrivial varieties of minimal rational tangents quasi-homogenous? We will show that this is not true in general, even when the projective manifold has Picard number 1. In fact, an isotrivial family of varieties of minimal rational tangents needs not be locally flat in differential geometric sense. This leads to the question for which projective variety Z, the Z-isotriviality of varieties of minimal rational tangents implies local flatness. Our main result verifies this for many cases of Z among complete intersections.Comment: Some errors in Section 8 and Lemma 8.1 corrected. To appear in The Asian Journal of Mathematics (AJM) special issue dedicated to Ngaiming Mok's 60th birthda

Vortex Structures in Model p-Wave Superconducting Sr2RuO4 -- Single 2-Dimensional Band v.s. Quasi-1-Dimensional Band

There have been an interesting debate on the primary source of chiral p-wave superconductivity in Sr2RuO4. We present a comparative study on the vortex structure between a single 2-dimensional (2D) band and quasi-1D band model by using Bogoliubov-de Gennes theory. The pattern of the iso-values of the local density of state around a vortex has a diamond shape in the quasi-1D model and is much more isotropic in the 2D model. The spin lattice relaxation rate well below the superconducting transition temperature is greatly enhanced in the vortex state in the 2D model but not in the quasi-1D model. These features can be tested by using scanning tunneling microscope and NMR to distinguish the models for the superconductivity in Sr2RuO4.Comment: 7 pages, 6 fig

On the structure of Enduk(2)(Ωk⊗r)End_{u_k(2)}(\Omega_k^{\otimes r})

Let $u_k(2)$ be the infinitesimal quantum $\frak{gl}_2$ over $k$, where $k$ is a field containing an $l$th primitive root $\epsilon$ of 1 with $l\geq 3$ {\it odd}. We will determine the basic algebra for ${u_k(2)}(\Omega_k^{\otimes r})$, where $\Omega_k$ is the natural module for $u_k(2)$