Gorenstein and normal properties of the subregular variety of a variety   of special lattices over Witt vectors
  We recall the projective variety parametrizing a family of special lattices over Witt vectors. It is normal and Gorenstein. In this article, we prove that there exists a particular set of subvarieties in it that are also normal and Gorenstein. The set contains the subregular variety. 
Akira Sano