Abstract
Let X ⊂ ℙ4 be an irreducible hypersurface and ε > 0 be given. We show that there are O(B3+ε), resp. O(B55/18+ε), rational points on ℙ4 lying on X when X is of degree d ⩾ 4, resp. d = 3. The implied constants depend only on d and ε.
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References
T. D. Browning — A note on the distribution of rational points on threefolds, Q. J. Math. 54 (2003), no. 1, 33–39.
W. Fulton & R. Lazarsfeld — Connectivity and its applications in algebraic geometry, Algebraic Geometry (Chicago, Ill., 1980), Lecture Notes in Math., vol. 862, Springer, Berlin, 1981, 26–92.
J. Harris — Algebraic Geometry, Graduate Texts in Mathematics, vol. 133, Springer-Verlag, New York, 1992.
D. R. Heath-Brown — The density of rational points on curves and surfaces, Ann. of Math. (2)155 (2002), no. 2, 553–595.
J. Pila — Density of integral and rational points on varieties, Astérisque (1995), no. 228, 4, 183–187, Columbia University Number Theory Seminar (New York, 1992).
W. M. Schmidt — Diophantine Approximations and Diophantine Equations, Lecture Notes in Mathematics, vol. 1467, Springer-Verlag, Berlin, 1991.
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Broberg, N., Salberger, P. (2004). Counting Rational Points On Threefolds. In: Poonen, B., Tschinkel, Y. (eds) Arithmetic of Higher-Dimensional Algebraic Varieties. Progress in Mathematics, vol 226. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8170-8_6
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DOI: https://doi.org/10.1007/978-0-8176-8170-8_6
Publisher Name: Birkhäuser, Boston, MA
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