# An overview of Manin's conjecture for del Pezzo surfaces

@article{Browning2005AnOO, title={An overview of Manin's conjecture for del Pezzo surfaces}, author={Tim D. Browning}, journal={arXiv: Number Theory}, year={2005} }

This paper surveys recent progress towards the Manin conjecture for (singular and non-singular) del Pezzo surfaces. To illustrate some of the techniques available, an upper bound of the expected order of magnitude is established for a singular del Pezzo surface of degree four.

## 44 Citations

### RESENT PROGRESS ON THE QUANTITATIVE ARITHMETIC OF DEL PEZZO SURFACES

- Mathematics
- 2009

— We survey the state of affairs for the distribution of Q-rational points on non-singular del Pezzo surfaces of low degree, highlighting the recent resolution of Manin’s conjecture for a…

### ON A CONSTANT ARISING IN MANIN'S CONJECTURE FOR DEL PEZZO SURFACES

- Mathematics
- 2007

For split smooth Del Pezzo surfaces, we analyse the structure of the effective cone and prove a recursive formula for the value of $\alpha$, appearing in the leading constant as predicted by Peyre of…

### Manin's conjecture on a nonsingular quartic del Pezzo surface

- Mathematics
- 2009

Given a nonsingular quartic del Pezzo surface, a conjecture of Manin predicts the density of rational points on the open subset of the surface formed by deleting the lines. We prove that this…

### Manin's conjecture for a singular quartic del Pezzo surface

- MathematicsJ. Lond. Math. Soc.
- 2012

Manin's conjecture for a split singular quartic del Pezzo surface with singularity type $2\Aone$ and eight lines is proved and a result of independent interest on a certain restricted divisor problem for four binary linear forms is proved.

### UNIVERSAL TORSORS OVER DEL PEZZO SURFACES AND RATIONAL POINTS

- Mathematics
- 2007

We discuss Manin's conjecture (with Peyre's refinement) concerning the distrib- ution of rational points of bounded height on Del Pezzo surfaces, by highlighting the use of universal torsors in such…

### Manin's conjecture for a quartic del Pezzo surface with A_4 singularity

- Mathematics
- 2007

The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type A_4.

### Manin’s conjecture for quartic Del Pezzo surfaces with a conic fibration

- Mathematics
- 2008

— An asymptotic formula is established for the number of Q-rational points of bounded height on a non-singular quartic del Pezzo surface with a conic bundle structure.

### Manin’s conjecture for a quartic del Pezzo surface with A3 singularity and four lines

- Mathematics
- 2010

We establish Manin’s conjecture for a quartic del Pezzo surface split over \({\mathbb{Q}}\) and having a singularity of type A3 and containing exactly four lines. It is the first example of split…

### Quantitative Arithmetic of Projective Varieties

- Mathematics
- 2009

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…

### Manin’s conjecture for a singular sextic del Pezzo surface

- Mathematics
- 2010

On demontre la conjecture de Manin pour une surface de del Pezzo de degre six qui a une singularite de type A 2 . De plus, on etablit un prolongement meromorphe et une expression explicite de la…

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