RATIONAL POINTS ON CERTAIN DEL PEZZO SURFACES OF DEGREE ONE
2008 ◽
Vol 50
(3)
◽
pp. 557-564
◽
Keyword(s):
AbstractLet$f(z)=z^5+az^3+bz^2+cz+d \in \Z[z]$and let us consider a del Pezzo surface of degree one given by the equation$\cal{E}_{f}\,{:}\,x^2-y^3-f(z)=0$. In this paper we prove that if the set of rational points on the curveEa,b:Y2=X3+ 135(2a−15)X−1350(5a+ 2b− 26) is infinite then the set of rational points on the surface ϵfis dense in the Zariski topology.
2016 ◽
Vol 152
(6)
◽
pp. 1198-1224
◽
2007 ◽
Vol 143
(3)
◽
pp. 579-605
◽
Keyword(s):
2011 ◽
Vol 07
(02)
◽
pp. 261-287
Keyword(s):
Keyword(s):
2017 ◽
Vol 153
(4)
◽
pp. 820-850
◽
2010 ◽
Vol 54
(1)
◽
pp. 187-219
◽
2017 ◽
Vol 13
(07)
◽
pp. 1895-1930
Keyword(s):
Keyword(s):
Keyword(s):
Keyword(s):