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arXiv · 1403.5937

Forms in many variables and differing degrees

T. D. Browning·D. R. Heath-Brown
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Abstract

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.

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T. D. Browning, D. R. Heath-Brown. 2015-02-02. Forms in many variables and differing degrees. https://arxiv.org/abs/1403.5937

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