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Abstract
Let X ⊂ ℙn be a projective geometrically integral variety over 
of dimension r and degree d ≧ 4. Suppose that there are only finitely many (r − 1)-planes over 
on X. The main result of this paper is a proof of the fact that the number N(X;B) of rational points on X which have height at most B satisfies 
for any ɛ > 0. The implied constant depends at most on d, n and ɛ.
Received: 2005-08-16
Revised: 2006-03-13
Published Online: 2007-08-07
Published in Print: 2007-06-27
© Walter de Gruyter
