RATIONAL POINTS ON CERTAIN DEL PEZZO SURFACES OF DEGREE ONE
Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 557-564

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Let and let us consider a del Pezzo surface of degree one given by the equation . In this paper we prove that if the set of rational points on the curve Ea,b : Y2 = X3 + 135(2a−15)X−1350(5a + 2b − 26) is infinite then the set of rational points on the surface εf is dense in the Zariski topology.
DOI : 10.1017/S0017089508004412
Mots-clés : Primary 11D25, 11D41, Secondary 11G052
ULAS, MACIEJ. RATIONAL POINTS ON CERTAIN DEL PEZZO SURFACES OF DEGREE ONE. Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 557-564. doi: 10.1017/S0017089508004412
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[1] 1.Bogomolov, F. and Tschinkel, Yu., On the density of rational points on elliptic fibrations, J. Reine und Angew. Math. 511 (1999), 87–93. Google Scholar | DOI

[2] 2.Connel, I., APECS: Arithmetic of plane elliptic curves, 2001, available from http://www.math.mcgill.ca/connell/public/apecs/. Google Scholar

[3] 3.Faltings, G., Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349–366. Google Scholar | DOI

[4] 4.Kuwata, M. and Wang, L., Topology of rational points on isotrivial elliptic surfaces, Int. Math. Research Notices 4 (1993), 113–123. Google Scholar | DOI

[5] 5.Manduchi, E., Root numbers of fibers of elliptic surfaces, Compos. Math. 99 (1995), 33–58. Google Scholar

[6] 6.Manin, Y. I., Cubic forms: Algebra, geometry, arithmetic, 2nd ed. (North-Holland Publishing, Amsterdam, 1986). Google Scholar

[7] 7.Munshi, R., Density of positive rank fibers in elliptic fibrations, J. Number Theory 125 (2007) 254–266. Google Scholar | DOI

[8] 8.Rohrlich, D. E., Variation of the root number in families of elliptic curves, Compos. Math. 87 (1993), 119–151. Google Scholar

[9] 9.Silverman, J., The arithmetic of elliptic curves (Springer-Verlag, New York, 1986). Google Scholar | DOI

[10] 10.Ulas, M., Rational points on certain elliptic surfaces, Acta Arith. 129 (2007), 167–185. Google Scholar | DOI

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