Table of contents for this issue | Previous article
Tim D. Browning; Ulrich Derenthal
Manin’s conjecture for a quartic del Pezzo surface with $\mathbf{A}_4$ singularity
(La conjecture de Manin pour une surface quartique de del Pezzo avec singularité $\mathbf{A}_4$)
Annales de l'institut Fourier, 59 no. 3 (2009), p. 1231-1265
Article: subscription required | Reviews MR 2543667
Class. Math.: 11G35, 14G05, 14G10
Keywords: Del Pezzo surfaces, rational points, Manin’s conjecture
[1] V. V. Batyrev & Yu. Tschinkel, “Manin’s conjecture for toric varieties”, J. Alg. Geom. 7 (1998), p. 15-53 MR 1620682 | Zbl 0946.14009
[2] R. de la Bretèche & T. D. Browning, “On Manin’s conjecture for singular del Pezzo surfaces of degree four, I”, Michigan Math. J. 55 (2007), p. 51-80
Article | MR 2320172 | Zbl 1132.14019
[3] T. D. Browning, An overview of Manin’s conjecture for del Pezzo surfaces, Analytic number theory — A tribute to Gauss and Dirichlet, Clay Math. Proceedings, 2007, p. 39–56 MR 2362193 | Zbl 1134.14017
[4] A. Chambert-Loir & Yu. Tschinkel, Fonctions zêta des hauteurs des espaces fibrés, in Birkhäuser, ed., Rational points on algebraic varieties, Progress in Math., 2001, p. 71–115 MR 1875171 | Zbl 1077.14524
[5] A. Chambert-Loir & Yu. Tschinkel, “On the distribution of points of bounded height on equivariant compactifications of vector groups”, Invent. Math. 148 (2002), p. 421-452 MR 1906155 | Zbl 1067.11036
[6] D. F. Coray & M. A. Tsfasman, “Arithmetic on singular del Pezzo surfaces”, Proc. London Math. Soc. 57 (1988), p. 25-87 MR 940430 | Zbl 0653.14018
[7] U. Derenthal, “Singular del Pezzo surfaces whose universal torsors are hypersurfaces”, arXiv:math.AG/0604194, 2006
arXiv
[8] U. Derenthal, “On a constant arising in Manin’s conjecture for del Pezzo surfaces”, Math. Res. Letters 14 (2007), p. 481-489 MR 2318651 | Zbl 1131.14042
[9] U. Derenthal, M. Joyce & Z. Teitler, “The nef cone volume of generalized del Pezzo surfaces”, Algebra & Number Theory 2 (2008), p. 157-182 MR 2377367 | Zbl pre05529322
[10] U. Derenthal & Yu. Tschinkel, Universal torsors over del Pezzo surfaces and rational points, Equidistribution in Number Theory, An Introduction, Springer, 2006 MR 2290499 | Zbl 1143.14017
[11] J. Franke, I. Manin & Yu. Tschinkel, “Rational points of bounded height on Fano varieties”, Invent. Math. 95 (1989), p. 421-435
Article | MR 974910 | Zbl 0674.14012
[12] B. Hassett & Yu. Tschinkel, “Geometry of equivariant compactifications of $\mathbf{G}_a^n$.”, Internat. Math. Res. Notices 22 (1999), p. 1211-1230 MR 1731473 | Zbl 0966.14033
[13] W. V. D. Hodge & D. Pedoe, Methods of algebraic geometry 2, Cambridge University Press, 1952 MR 48065
[14] E. Peyre, “Hauteurs et nombres de Tamagawa sur les variétés de Fano”, Duke Math. J. 79 (1995), p. 101-218
Article | MR 1340296 | Zbl 0901.14025
[15] P. Salberger, “Tamagawa measures on universal torsors and points of bounded height on Fano varieties”, Astérisque 251 (1998), p. 91-258 MR 1679841 | Zbl 0959.14007
Tim D. Browning; Ulrich Derenthal
Manin’s conjecture for a quartic del Pezzo surface with $\mathbf{A}_4$ singularity
(La conjecture de Manin pour une surface quartique de del Pezzo avec singularité $\mathbf{A}_4$)
Annales de l'institut Fourier, 59 no. 3 (2009), p. 1231-1265
Article: subscription required | Reviews MR 2543667
Class. Math.: 11G35, 14G05, 14G10
Keywords: Del Pezzo surfaces, rational points, Manin’s conjecture
Résumé - Abstract
The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type $\mathbf{A}_4$.
Bibliography
[2] R. de la Bretèche & T. D. Browning, “On Manin’s conjecture for singular del Pezzo surfaces of degree four, I”, Michigan Math. J. 55 (2007), p. 51-80
Article | MR 2320172 | Zbl 1132.14019
[3] T. D. Browning, An overview of Manin’s conjecture for del Pezzo surfaces, Analytic number theory — A tribute to Gauss and Dirichlet, Clay Math. Proceedings, 2007, p. 39–56 MR 2362193 | Zbl 1134.14017
[4] A. Chambert-Loir & Yu. Tschinkel, Fonctions zêta des hauteurs des espaces fibrés, in Birkhäuser, ed., Rational points on algebraic varieties, Progress in Math., 2001, p. 71–115 MR 1875171 | Zbl 1077.14524
[5] A. Chambert-Loir & Yu. Tschinkel, “On the distribution of points of bounded height on equivariant compactifications of vector groups”, Invent. Math. 148 (2002), p. 421-452 MR 1906155 | Zbl 1067.11036
[6] D. F. Coray & M. A. Tsfasman, “Arithmetic on singular del Pezzo surfaces”, Proc. London Math. Soc. 57 (1988), p. 25-87 MR 940430 | Zbl 0653.14018
[7] U. Derenthal, “Singular del Pezzo surfaces whose universal torsors are hypersurfaces”, arXiv:math.AG/0604194, 2006
arXiv
[8] U. Derenthal, “On a constant arising in Manin’s conjecture for del Pezzo surfaces”, Math. Res. Letters 14 (2007), p. 481-489 MR 2318651 | Zbl 1131.14042
[9] U. Derenthal, M. Joyce & Z. Teitler, “The nef cone volume of generalized del Pezzo surfaces”, Algebra & Number Theory 2 (2008), p. 157-182 MR 2377367 | Zbl pre05529322
[10] U. Derenthal & Yu. Tschinkel, Universal torsors over del Pezzo surfaces and rational points, Equidistribution in Number Theory, An Introduction, Springer, 2006 MR 2290499 | Zbl 1143.14017
[11] J. Franke, I. Manin & Yu. Tschinkel, “Rational points of bounded height on Fano varieties”, Invent. Math. 95 (1989), p. 421-435
Article | MR 974910 | Zbl 0674.14012
[12] B. Hassett & Yu. Tschinkel, “Geometry of equivariant compactifications of $\mathbf{G}_a^n$.”, Internat. Math. Res. Notices 22 (1999), p. 1211-1230 MR 1731473 | Zbl 0966.14033
[13] W. V. D. Hodge & D. Pedoe, Methods of algebraic geometry 2, Cambridge University Press, 1952 MR 48065
[14] E. Peyre, “Hauteurs et nombres de Tamagawa sur les variétés de Fano”, Duke Math. J. 79 (1995), p. 101-218
Article | MR 1340296 | Zbl 0901.14025
[15] P. Salberger, “Tamagawa measures on universal torsors and points of bounded height on Fano varieties”, Astérisque 251 (1998), p. 91-258 MR 1679841 | Zbl 0959.14007
© Annales de L'Institut Fourier - ISSN (électronique) : 1777-5310