2009/05/31 by Oscar Marmon, O. Marmon · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Mathematics and Applications #Polynomial and algebraic computation #math.NT #msc:11G35
paper · pdf · doi:10.1007/s10958-010-0178-5
published as Journal of Mathematical Sciences: Volume 171, Issue 6 (2010), Page 736 · 13 pages
openalex publication_date 2010/11/18 · crossref created 2010/11/18 · crossref issued 2010/11/19 · crossref published 2010/11/19 · crossref published-online 2010/11/19 · crossref published-print 2010/12/01 · arxiv created 2010/12/22 · arxiv updated 2010/12/23 · crossref deposited 2019/06/02 · crossref indexed 2024/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.