Quantitative Arithmetic of Projective Varieties / by Timothy D. Browning.

Springer eBooks

The Manin conjectures -- The dimension growth conjecture -- Uniform bounds for curves and surfaces -- A1 del Pezzo surface of degree 6 -- D4 del Pezzo surface of degree 3 -- Siegel’s lemma and non-singular surfaces -- The Hardy—Littlewood circle method.

This monograph is concerned with counting rational points of bounded height on projective algebraic varieties. This is a relatively young topic, whose exploration has already uncovered a rich seam of mathematics situated at the interface of analytic number theory and Diophantine geometry. The goal of the book is to give a systematic account of the field with an emphasis on the role played by analytic number theory in its development. Among the themes discussed in detail are * the Manin conjecture for del Pezzo surfaces; * Heath-Brown's dimension growth conjecture; and * the Hardy-Littlewood circle method. Readers of this monograph will be rapidly brought into contact with a spectrum of problems and conjectures that are central to this fertile subject area.

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