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.
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.
Quantitative Arithmetic of Projective Varieties
160
Quantitative Arithmetic of Projective Varieties
160Hardcover(2010)
Product Details
| ISBN-13: | 9783034601283 |
|---|---|
| Publisher: | Birkh�user Basel |
| Publication date: | 10/23/2009 |
| Series: | Progress in Mathematics , #277 |
| Edition description: | 2010 |
| Pages: | 160 |
| Product dimensions: | 6.20(w) x 9.20(h) x 0.60(d) |