TY - JOUR
AB - 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 X Pm, provided only that its dimension is large enough in terms of its degree.
AU - Browning, Timothy D
AU - Heath Brown, Roger
ID - 266
IS - 2
JF - Journal of the European Mathematical Society
TI - Forms in many variables and differing degrees
VL - 19
ER -