Type: Article
Publication Date: 2017-01-26
Citations: 37
DOI: https://doi.org/10.4171/jems/668
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 \subseteq \mathbb P^m , provided only that its dimension is large enough in terms of its degree.