Constructing Q-Fano 3-folds à la Prokhorov & Reid

Abstract

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.

15 pages

References in corpus (4)

• Fano 3-folds in codimension 4, Tom and Jerry, Part I
• Ice cream and orbifold Riemann-Roch
• On Q-Fano threefolds of Fano index 2
• Divisorial Extractions from Singular Curves in Smooth 3-Folds, I