no. 1
Counting rational points on hypersurfaces of low dimension
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 1, pp. 93-115. 
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     title = {Counting rational points on hypersurfaces of low dimension},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
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     zbl = {1110.14020},
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     url = {http://www.numdam.org/articles/10.1016/j.ansens.2004.10.005/}
}
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Salberger, Per. Counting rational points on hypersurfaces of low dimension. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 1, pp. 93-115. doi : 10.1016/j.ansens.2004.10.005. http://www.numdam.org/articles/10.1016/j.ansens.2004.10.005/

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

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

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

[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

[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 | Zbl

[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 | Zbl

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

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

[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

[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

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

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

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

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

[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 | Zbl

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

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

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

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

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

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

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

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

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

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

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

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