Counting rational points on hypersurfaces of low dimension
Salberger, Per
Annales scientifiques de l'École Normale Supérieure, Tome 38 (2005), p. 93-115 / Harvested from Numdam
@article{ASENS_2005_4_38_1_93_0,
     author = {Salberger, Per},
     title = {Counting rational points on hypersurfaces of low dimension},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {38},
     year = {2005},
     pages = {93-115},
     doi = {10.1016/j.ansens.2004.10.005},
     mrnumber = {2136483},
     zbl = {1110.14020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2005_4_38_1_93_0}
}
Salberger, Per. Counting rational points on hypersurfaces of low dimension. Annales scientifiques de l'École Normale Supérieure, Tome 38 (2005) pp. 93-115. doi : 10.1016/j.ansens.2004.10.005. http://gdmltest.u-ga.fr/item/ASENS_2005_4_38_1_93_0/

[1] Barth W., Peters C., Van De Ven A., Compact Complex Surfaces, Springer-Verlag, New York, 1984. | MR 749574 | Zbl 0718.14023

[2] Beltrametti M.C., Sommese A.J., Adjunction Theory of Complex Projective Varieties, De Gruyter, Berlin, 1995. | MR 1318687 | Zbl 0845.14003

[3] Bombieri E., Pila J., The number of integral points on arcs and ovals, Duke Math. J. 59 (1989) 337-357. | MR 1016893 | Zbl 0718.11048

[4] Broberg N., A note on a paper by R. Heath-Brown: “The density of rational points on curves and surfaces”, J. Reine Angewandte Math. 571 (2004) 159-178. | Zbl 1053.11027

[5] Broberg N., Salberger P., Counting rational points on threefolds, in: Poonen B., Tschinkel Y. (Eds.), Arithmetic of Higher-Dimensional Varieties, Progress in Mathematics, vol. 206, Birkhäuser, Boston, 2003. | MR 2029864 | Zbl 02158895

[6] Bruce J.W., Wall C.T.C., On the classification of cubic surfaces, J. London Math. Soc. II Ser. 19 (1979) 245-256. | MR 533323 | Zbl 0393.14007

[7] Browning T.D., A note on the distribution of rational points in threefolds, Quart. J. Math. 54 (2003) 33-39. | MR 1967067 | Zbl 1076.14514

[8] Browning T.D., Heath-Brown R., Equal sums of three powers, Invent. Math. 157 (2004) 553-573. | MR 2092769 | Zbl 02104979

[9] Castelnuovo G., Sulle superficie algebriche che ammettono un sistema doppiamento infinito di sezioni piani riducibili, Rend. R. Accademia dei Lincei s. V III (1) (1894). | JFM 25.1228.02

[10] Colliot-Thélène J.-L., Appendix to Heath-Brown's paper “The density of rational points on curves and surfaces”, Ann. of Math. 155 (2002) 596-598. | Zbl 1039.11044

[11] Davenport H., Analytic Methods for Diophantine Equations and Diophantine Inequalities, Ann Arbor Publishers, Ann Arbor, 1962. | MR 159786 | Zbl 1089.11500

[12] Debarre O., Higher-Dimensional Algebraic Geometry, Springer, New York, 2001. | MR 1841091 | Zbl 0978.14001

[13] Eisenbud D., Harris J., The Geometry of Schemes, Graduate Texts in Math., vol. 197, Springer-Verlag, New York, 2000. | MR 1730819 | Zbl 0960.14002

[14] Fulton W., Intersection Theory, Springer-Verlag, Berlin, 1984. | MR 732620 | Zbl 0541.14005

[15] Fulton W., Lazarsfeld R., Connectivity and its applications in algebraic geometry, in: Algebraic Geometry, Lecture Notes in Mathematics, vol. 862, Springer-Verlag, Berlin, pp. 26-92. | MR 644817 | Zbl 0484.14005

[16] Harris J., Algebraic Geometry, Graduate Texts in Math., vol. 133, Springer-Verlag, New York, 1995. | MR 1416564 | Zbl 0779.14001

[17] Hartshorne R., Algebraic Geometry, Graduate Texts in Math., vol. 52, Springer-Verlag, New York, 1977. | MR 463157 | Zbl 0367.14001

[18] Hartshorne R., Ample Subvarieties of Algebraic Varieties, Lecture Notes in Mathematics, vol. 156, Springer-Verlag, Berlin. | MR 282977 | Zbl 0208.48901

[19] Heath-Brown R., The density of rational points on curves and surfaces, Ann. of Math. 155 (2002) 553-595. | MR 1906595 | Zbl 1039.11044

[20] Hua L.-K., On Waring's problem, Quart. J. Math. Oxford Ser. 9 (1938) 199-202. | JFM 64.0124.04

[21] Jouanolou J.P., Théorèmes de Bertini et Applications, Progress in Math., vol. 42, Birkhäuser, Boston, 1983. | MR 725671 | Zbl 0519.14002

[22] Katz N., Exposé XVII, SGA 7 II, Springer-Verlag, Berlin, 1973. | MR 354657

[23] Pila J., Density of integral and rational points on varieties, Astérisque 228 (1995) 183-187. | MR 1330933 | Zbl 0834.11028

[24] Pila J., Density of integral points on plane algebraic curves, Internat. Math. Res. Notices 96 (1996) 903-912. | MR 1420555 | Zbl 0973.11085

[25] Ueno K., Classification of algebraic manifolds, in: Proc. of the International Congress of Mathematicians, Helsinki, 1978, pp. 549-556. | MR 562654 | Zbl 0461.14008

[26] Zak F.L., Tangents and Secants of Algebraic Varieties, Translations of Mathematical Monographs, vol. 127, American Mathematical Society, Providence, RI, 1983. | MR 1234494 | Zbl 0795.14018