Journal of the Ramanujan Mathematical Society

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Potential Density for Some Families of Homogeneous Spaces


Affiliations
1 CNRS, UMR 8628, Mathematiques, Batiment 425, Universite Paris-Sud, F-91405 Orsay, France
2 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India
     

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For a smooth, projective family of homogeneous varieties defined over a number field, we show that if potential density holds for the rational points of the base, then it also holds for the total space. A conjecture of Campana and Peternell, known in dimension at most 4 and for certain higher dimensional cases, would then imply potential density for the rational points of smooth projective varieties over number fields whose tangent bundle is nef.
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  • Potential Density for Some Families of Homogeneous Spaces

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Authors

J. L. Colliot-Thelene
CNRS, UMR 8628, Mathematiques, Batiment 425, Universite Paris-Sud, F-91405 Orsay, France
J. N. Iyer
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India

Abstract


For a smooth, projective family of homogeneous varieties defined over a number field, we show that if potential density holds for the rational points of the base, then it also holds for the total space. A conjecture of Campana and Peternell, known in dimension at most 4 and for certain higher dimensional cases, would then imply potential density for the rational points of smooth projective varieties over number fields whose tangent bundle is nef.