Manin’s conjecture for a quartic del Pezzo surface with A 4 singularity

Tim D. Browning[1]; Ulrich Derenthal[2]

  • [1] University of Bristol School of Mathematics Bristol BS8 1TW (United Kingdom)
  • [2] Universität Zürich Institut für Mathematik Winterthurerstrasse 190 8057 Zürich (Switzerland)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 3, page 1231-1265
  • ISSN: 0373-0956

Abstract

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The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type A 4 .

How to cite

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Browning, Tim D., and Derenthal, Ulrich. "Manin’s conjecture for a quartic del Pezzo surface with $\mathbf{A}_4$ singularity." Annales de l’institut Fourier 59.3 (2009): 1231-1265. <http://eudml.org/doc/10421>.

@article{Browning2009,
abstract = {The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type $\mathbf\{A\}_4$.},
affiliation = {University of Bristol School of Mathematics Bristol BS8 1TW (United Kingdom); Universität Zürich Institut für Mathematik Winterthurerstrasse 190 8057 Zürich (Switzerland)},
author = {Browning, Tim D., Derenthal, Ulrich},
journal = {Annales de l’institut Fourier},
keywords = {Del Pezzo surfaces; rational points; Manin’s conjecture; del Pezzo surfaces; Manin's conjecture; Diophantine equations},
language = {eng},
number = {3},
pages = {1231-1265},
publisher = {Association des Annales de l’institut Fourier},
title = {Manin’s conjecture for a quartic del Pezzo surface with $\mathbf\{A\}_4$ singularity},
url = {http://eudml.org/doc/10421},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Browning, Tim D.
AU - Derenthal, Ulrich
TI - Manin’s conjecture for a quartic del Pezzo surface with $\mathbf{A}_4$ singularity
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 3
SP - 1231
EP - 1265
AB - The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type $\mathbf{A}_4$.
LA - eng
KW - Del Pezzo surfaces; rational points; Manin’s conjecture; del Pezzo surfaces; Manin's conjecture; Diophantine equations
UR - http://eudml.org/doc/10421
ER -

References

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  3. T. D. Browning, An overview of Manin’s conjecture for del Pezzo surfaces, Analytic number theory — A tribute to Gauss and Dirichlet 7 (2007), 39-56, Clay Math. Proceedings Zbl1134.14017MR2362193
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  9. U. Derenthal, M. Joyce, Z. Teitler, The nef cone volume of generalized del Pezzo surfaces, Algebra & Number Theory 2 (2008), 157-182 Zbl1158.14032MR2377367
  10. U. Derenthal, Yu. Tschinkel, Universal torsors over del Pezzo surfaces and rational points, Equidistribution in Number Theory, An Introduction 237 (2006), Springer Zbl1143.14017MR2290499
  11. J. Franke, I. Manin, Yu. Tschinkel, Rational points of bounded height on Fano varieties, Invent. Math. 95 (1989), 421-435 Zbl0674.14012MR974910
  12. B. Hassett, Yu. Tschinkel, Geometry of equivariant compactifications of G a n ., Internat. Math. Res. Notices 22 (1999), 1211-1230 Zbl0966.14033MR1731473
  13. W. V. D. Hodge, D. Pedoe, Methods of algebraic geometry, 2 (1952), Cambridge University Press Zbl0048.14502MR48065
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  15. P. Salberger, Tamagawa measures on universal torsors and points of bounded height on Fano varieties, Astérisque 251 (1998), 91-258 Zbl0959.14007MR1679841

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