Rational Double Points on a Rational Surface.
N. Mohan Kumar (1981/82)
Inventiones mathematicae
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N. Mohan Kumar (1981/82)
Inventiones mathematicae
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F. Campana, H. Flenner (1993)
Journal für die reine und angewandte Mathematik
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Andrey Trepalin (2014)
Open Mathematics
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Let be a field of characteristic zero and G be a finite group of automorphisms of projective plane over . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field is algebraically closed. In this paper we prove that is rational for an arbitrary field of characteristic zero.
Lucian Badescu (1986)
Journal für die reine und angewandte Mathematik
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Biswas, Indranil, Huisman, Johannes (2007)
Documenta Mathematica
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Tim Browning, Michael Swarbrick Jones (2014)
Acta Arithmetica
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For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.
Gianni Sacchiero (1982)
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E. Ballico, R. Piene, H.-S. Tai (1992)
Mathematica Scandinavica
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Marco Manetti (1993)
Rendiconti del Seminario Matematico della Università di Padova
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J. Achari (1978)
Matematički Vesnik
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Antonio Cafure, Guillermo Matera (2007)
Acta Arithmetica
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Bianca Viray (2010)
Journal de Théorie des Nombres de Bordeaux
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We construct a concrete example of a -parameter family of smooth projective geometrically integral varieties over an open subscheme of such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.