Q-factorial quartic threefolds

Abstract

We prove that a nodal quartic threefold $X$ containing no planes is $Q$-factorial provided that it has not more than 12 singular points, with the exception of a quartic with exactly 12 singularities containing a quadric surface. We give some geometrical constructions related to the latter quartic.

13 pages; minor corrections

Cited by in corpus (2)

• Birational automorphisms of nodal quartic threefolds
• Birational rigidity and Q-factoriality of a singular double quadric