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ON THE NUMBER OF RATIONAL POINTS OF BOUNDED HEIGHT ON SMOOTH BILINEAR HYPERSURFACES IN BIPROJECTIVE SPACE

Published online by Cambridge University Press:  19 March 2001

MARCELLO ROBBIANI
MARCELLO ROBBIANI
Affiliation:
ETH Zürich, Mathematik, CH-8092 Zürich, Switzerland; [email protected]@zhwin.ch
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Abstract

Asymptotic formulae for the number of rational points of bounded height on flag varieties have earlier been established. In the paper these asymptotic formulae are recovered by a new method for varieties in biprojective space defined over ℚ that are isomorphic to the flag variety of lines in hyperplanes.

The result is obtained by an application of Heath-Brown's new form of the circle method. It serves as a pointer to the investigation of rational points of bounded height on varieties in multiprojective space.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 33 - 51
Copyright
The London Mathematical Society 2001

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