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Paper detail

Forms in many variables and differing degrees

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 projective variety, provided only that its dimension is large enough in terms of its degree.

preprint2015arXivOpen access
T. D. BrowningD. R. Heath-Brown
math.AGmath.NT
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T. D. BrowningD. R. Heath-Brown

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