New York Journal of Mathematics
Volume 28 (2022), 1193-1229


Tim Browning

Revisiting the Manin--Peyre conjecture for the split del Pezzo surface of degree 5

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Published: August 24, 2022.
Keywords: del Pezzo surface, conic bundle, rational points, height function, divisor sum problem, lattice points.
Subject [2010]: 11G35, 14G05, 14J45.

An improved asymptotic formula is established for the number of rational points of bounded height on the split smooth del Pezzo surface of degree 5. The proof uses the five conic bundle structures on the surface.


This work was begun while the author was participating in the programme on "Diophantine equations" at the Hausdorff Research Institute for Mathematics in Bonn in 2009. The hospitality and financial support of the institute is gratefully acknowledged. The idea of using conic bundles to study the split del Pezzo surface of degree 5 was explained to the author by Professor Salberger. The author is very grateful to him for his input into this project and also to Shuntaro Yamagishi for many useful comments on an earlier version of this manuscript. While working on this paper the author was supported by FWF grant P32428-N35.

Author information

Tim Browning:
IST Austria
Am Campus 1
3400 Klosterneuburg, Austria