A generalization of the Bombieri-Pila determinant method

Abstract

The so-called determinant method was developed by Bombieri and Pila in 1989 for counting integral points of bounded height on affine plane curves. In this paper we give a generalization of that method to varieties of higher dimension, yielding a proof of Heath-Brown's 'Theorem 14' by real-analytic considerations alone.

13 pages

References in corpus (2)

• The density of rational points in curves and surfaces
• A Proof of Gromov's Algebraic Lemma

Cited by in corpus (4)

• Points on curves in small boxes en applications
• Smooth Parametrizations in Dynamics, Analysis, Diophantine and Computational Geometry
• Non-archimedean Yomdin-Gromov parametrizations and points of bounded height
• Complex Cellular Structures