Abstract:
We prove that a general three-dimensional quartic $V$ in the complex
projective space ${\mathbb P}^4$, the only singularity of which is a double
point of rank 3, is a birationally rigid variety. Its group of birational
self-maps is, up to the finite subgroup of biregular automorphisms, a free
product of 25 cyclic groups of order 2. It follows that the complement to the
set of birationally rigid factorial quartics with terminal singularities is of
codimension at least 3 in the natural parameter space.
