K3 surfaces with Picard number three and canonical vector heights
نویسندگان
چکیده
منابع مشابه
K3 surfaces with Picard number three and canonical vector heights
In this paper we construct the first known explicit family of K3 surfaces defined over the rationals that are proved to have geometric Picard number 3. This family is dense in one of the components of the moduli space of all polarized K3 surfaces with Picard number at least 3. We also use an example from this family to fill a gap in an earlier paper by the first author. In that paper, an argume...
متن کاملCanonical vector heights on K3 surfaces with Picard number three - An argument for nonexistence
In this paper, we investigate a K3 surface with Picard number three and present evidence that strongly suggests a canonical vector height cannot exist on this surface.
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In an earlier paper by the first author, an argument for the nonexistence of canonical vector heights on K3 surfaces of Picard number three was given, based on an explicit surface that was not proved to have Picard number three. In this paper, we fill the gap in the argument by redoing the computations for another explicit surface for which we prove that the Picard number equals three. The conc...
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A long-standing question in the theory of rational points of algebraic surfaces is whether a K3 surface X over a number field K acquires a Zariski-dense set of L-rational points over some finite extension L/K. In this case, we say X has potential density of rational points. In case XC has Picard rank greater than 1, Bogomolov and Tschinkel [2] have shown in many cases that X has potential densi...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2007
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-07-01962-x