Rational points on pencils of conics and quadrics with many degenerate   fibres
  For any pencil of conics or higher-dimensional quadrics over the rationals, with all degenerate fibres defined over the rationals, we show that the Brauer-Manin obstruction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics, which is a consequence of recent advances in additive combinatorics. 
Tim Browning, Lilian Matthiesen, Alexei Skorobogatov
math.NT math.AG