Hilbert Schemes and Toric Degenerations for Low Degree Fano Threefolds
  For fixed degree $d\leq 12$, we study the Hilbert scheme of degree $d$ smooth Fano threefolds in their anticanonical embeddings. We use this to classify all possible degenerations of these varieties to toric Fano varieties with at most canonical Gorenstein singularities. 
Jan Arthur Christophersen and Nathan Owen Ilten
math.AG