Counting rational points on hypersurfaces of low dimension

 Access to full text

 Full (PDF)

1. [1] Barth W., Peters C., Van de Ven A., Compact Complex Surfaces, Springer-Verlag, New York, 1984. Zbl0718.14023MR749574
2. [2] Beltrametti M.C., Sommese A.J., Adjunction Theory of Complex Projective Varieties, De Gruyter, Berlin, 1995. Zbl0845.14003MR1318687
3. [3] Bombieri E., Pila J., The number of integral points on arcs and ovals, Duke Math. J.59 (1989) 337-357. Zbl0718.11048MR1016893
4. [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. Zbl1053.11027
5. [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. Zbl1151.11328MR2029864
6. [6] Bruce J.W., Wall C.T.C., On the classification of cubic surfaces, J. London Math. Soc. II Ser.19 (1979) 245-256. Zbl0393.14007MR533323
7. [7] Browning T.D., A note on the distribution of rational points in threefolds, Quart. J. Math.54 (2003) 33-39. Zbl1076.14514MR1967067
8. [8] Browning T.D., Heath-Brown R., Equal sums of three powers, Invent. Math.157 (2004) 553-573. Zbl1135.11052MR2092769
9. [9] Castelnuovo G., Sulle superficie algebriche che ammettono un sistema doppiamento infinito di sezioni piani riducibili, Rend. R. Accademia dei Lincei s. VIII (1) (1894). JFM25.1228.02
10. [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. Zbl1039.11044
11. [11] Davenport H., Analytic Methods for Diophantine Equations and Diophantine Inequalities, Ann Arbor Publishers, Ann Arbor, 1962. Zbl1089.11500MR159786
12. [12] Debarre O., Higher-Dimensional Algebraic Geometry, Springer, New York, 2001. Zbl0978.14001MR1841091
13. [13] Eisenbud D., Harris J., The Geometry of Schemes, Graduate Texts in Math., vol. 197, Springer-Verlag, New York, 2000. Zbl0960.14002MR1730819
14. [14] Fulton W., Intersection Theory, Springer-Verlag, Berlin, 1984. Zbl0541.14005MR732620
15. [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. Zbl0484.14005MR644817
16. [16] Harris J., Algebraic Geometry, Graduate Texts in Math., vol. 133, Springer-Verlag, New York, 1995. Zbl0779.14001MR1416564
17. [17] Hartshorne R., Algebraic Geometry, Graduate Texts in Math., vol. 52, Springer-Verlag, New York, 1977. Zbl0367.14001MR463157
18. [18] Hartshorne R., Ample Subvarieties of Algebraic Varieties, Lecture Notes in Mathematics, vol. 156, Springer-Verlag, Berlin. Zbl0208.48901MR282977
19. [19] Heath-Brown R., The density of rational points on curves and surfaces, Ann. of Math.155 (2002) 553-595. Zbl1039.11044MR1906595
20. [20] Hua L.-K., On Waring's problem, Quart. J. Math. Oxford Ser.9 (1938) 199-202. Zbl64.0124.04JFM64.0124.04
21. [21] Jouanolou J.P., Théorèmes de Bertini et Applications, Progress in Math., vol. 42, Birkhäuser, Boston, 1983. Zbl0519.14002MR725671
22. [22] Katz N., Exposé XVII, SGA 7 II, Springer-Verlag, Berlin, 1973. MR354657
23. [23] Pila J., Density of integral and rational points on varieties, Astérisque228 (1995) 183-187. Zbl0834.11028MR1330933
24. [24] Pila J., Density of integral points on plane algebraic curves, Internat. Math. Res. Notices96 (1996) 903-912. Zbl0973.11085MR1420555
25. [25] Ueno K., Classification of algebraic manifolds, in: Proc. of the International Congress of Mathematicians, Helsinki, 1978, pp. 549-556. Zbl0461.14008MR562654
26. [26] Zak F.L., Tangents and Secants of Algebraic Varieties, Translations of Mathematical Monographs, vol. 127, American Mathematical Society, Providence, RI, 1983. Zbl0795.14018MR1234494