Abstract:
Let K be a number field and its ring of integers. Let be a Hermitian vector bundle over . In the first part of this paper we estimate the number of points of bounded height in (generalizing a result by Schanuel). We give then some applications: we estimate the number of hyperplanes and hypersurfaces of degree d>1 in of bounded height and containing a fixed linear subvariety and we estimate the number of points of height, with respect to the anticanonical line bundle, less then T (when T goes to infinity) of ℙN K blown up at a linear subspace of codimension two.
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Received: 20 February 1998 / Revised version: 9 November 1998
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Gasbarri, C. On the number of points of bounded height¶on arithmetic projective spaces. manuscripta math. 98, 453–475 (1999). https://doi.org/10.1007/s002290050153
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DOI: https://doi.org/10.1007/s002290050153