Some non-finitely generated Cox rings
  We give a large family of weighted projective planes, blown up at a smooth point, that do not have finitely generated Cox rings. We then use the method of Castravet and Tevelev to prove that the moduli space of stable n-pointed genus zero curves does not have a finitely generated Cox ring if n is at least 13. 
Jos\'e Luis Gonz\'alez and Kalle Karu
math.AG math.AC