Constructing Q-Fano 3-folds \`a la Prokhorov & Reid
  We generalise a construction by Prokhorov & Reid of two families of Q-Fano 3-folds of index 2 to obtain five more families of Q-Fano 3-folds; four of index 2 and one of index 3. Two of the families constructed have the same Hilbert series and we study these cases in more detail. 
Tom Ducat
math.AG