Weak approximation on del Pezzo surfaces of degree 1

We study del Pezzo surfaces of degree 1 of the formw2=z3+Ax6+By6w2=z3+Ax6+By6 in the weighted projective space Pk(1,1,2,3)Pk(1,1,2,3), where k   is a perfect field of characteristic not 2 or 3 and A,B∈k∗A,B∈k∗. Over a number field, we exhibit an infinite family of (minimal) counterexamples to weak approximation amongst these surfaces, via a Brauer–Manin obstruction.