Standard conjectures for the arithmetic Grassmannian G(2,N) and Racah polynomials

Arithmetic infinite Grassmannians and the induced central extensions

The construction of families of Sato Grassmannians, their determinant line bundles and the extensions induced by them are given. The base scheme is an arbitrary scheme.

Arithmetic fake projective spaces and arithmetic fake grassmannians

We show that if n>5, PU(n-1,1) does not contain a cocompact arithmetic subgroup with the same Euler-Poincare characteristic (in the sense of C.T.C. Wall) as the complex projective space of dimension n-1, and show that if n=5, there are at least four such subgroups, which are in fact torsion-free. This, in particular, leads to examples of a fake projective space of dimension 4. Analogous results for arithmetic fake grassmannians Gr(m,n) with n>3 odd are also obtained.

高度对称的Calabi-Yau Grassmannian超曲面的形变

Deformations of highly symmetric Calabi-Yau Grassmannian hypersurfaces

本文运用算术与Hodge理论技术研究Grassmannians及其商空间中高度对称超曲面实现的Calabi-Yau簇的铅笔，证明其几何性质不同于经典镜像。