Forms in many variables and differing degrees

  • Tim D. Browning

    University of Bristol, UK
  • David Rodney Heath-Brown

    Oxford University, UK


We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin–Peyre conjecture for a smooth and geometrically integral variety , provided only that its dimension is large enough in terms of its degree.

Cite this article

Tim D. Browning, David Rodney Heath-Brown, Forms in many variables and differing degrees. J. Eur. Math. Soc. 19 (2017), no. 2, pp. 357–394

DOI 10.4171/JEMS/668