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arxiv: 1403.5937 · v2 · pith:LQ6ESIG2new · submitted 2014-03-24 · 🧮 math.NT · math.AG

Forms in many variables and differing degrees

T.D. Browning , D.R. Heath-Brown This is my paper
classification 🧮 math.NT math.AG
keywords formsdegreesmanyvariablesallowsapproximationbirchconjecture
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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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