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arXiv · 2412.05205

Slope-determinant method, complex cellular structures and hypersurface coverings of regular rational points

Kenneth Chung Tak Chiu
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Abstract

We use the determinant method of Bombieri-Pila and Heath-Brown and its Arakelov reformulation by Chen utilizing Bost's slope method to estimate the number of hypersurfaces required to cover the regular rational points with bounded Arakelov height on a projective variety. Using complex cellular structures introduced by Binyamini-Novikov, we replace the usual subpolynomial factor by a polylogarithmic factor in the estimation.

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Kenneth Chung Tak Chiu. 2024-12-06. Slope-determinant method, complex cellular structures and hypersurface coverings of regular rational points. https://arxiv.org/abs/2412.05205

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