The boundary of the moduli space of stable cubic fivefolds
  According to Mumford's geometric invariant theory, the moduli space of stable cubic fivefolds is compactified by adding nonstable semi-stable (i.e., strictly semi-stable) locus. In this paper, we prove that this locus consists of 21 irreducible components. Moreover, we give a description of equation and singularity of the cubic fivefold corresponding to the generic point in each component. 
Yasutaka Shibata
math.AG