Universal torsors over Del Pezzo surfaces and rational points

Details Universal torsors over Del Pezzo surfaces and rational points Universal torsors over Del Pezzo surfaces and rational points

2006-04-09

arxiv.org/abs/math/0604193v1

Mathematics

Number Theory

33 pages, 2 figures

Scientific paper

We discuss Manin's conjecture concerning the distribution of rational points of bounded height on Del Pezzo surfaces, and its refinement by Peyre, and explain applications of universal torsors to counting problems. To illustrate the method, we provide a proof of Manin's conjecture for the unique split singular quartic Del Pezzo surface with a singularity of type D4. (Lectures at the summer school "Equidistribution in number theory", Montreal, August 2005)

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