Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5
Browning TD. 2022. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. 28, 1193–1229.
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Abstract
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.
Publishing Year
Date Published
2022-08-24
Journal Title
New York Journal of Mathematics
Acknowledgement
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.
Volume
28
Page
1193 - 1229
ISSN
IST-REx-ID
Cite this
Browning TD. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. 2022;28:1193-1229.
Browning, T. D. (2022). Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. State University of New York.
Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del Pezzo Surface of Degree 5.” New York Journal of Mathematics. State University of New York, 2022.
T. D. Browning, “Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5,” New York Journal of Mathematics, vol. 28. State University of New York, pp. 1193–1229, 2022.
Browning TD. 2022. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. 28, 1193–1229.
Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del Pezzo Surface of Degree 5.” New York Journal of Mathematics, vol. 28, State University of New York, 2022, pp. 1193–229.
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