  A known conjecture of Grinenko in birational geometry asserts that a Mori
fibre space with the structure of del Pezzo fibration of low degree is
birationally rigid if and only if its anticanonical class is an interior point
in the cone of mobile divisors. The conjecture is proved to be true for smooth
models (with a generality assumption for degree 3). It is speculated that the
conjecture holds for, at least, Gorenstein models in degree 1 and 2. In this
article, I present a (Gorenstein) counterexample in degree 2 to this
conjecture.
