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Mumford's Degree of Contact and Diophantine Approximations

Published online by Cambridge University Press:  04 December 2007

Roberto G. Ferretti
Roberto G. Ferretti
Affiliation:
Departement Mathematik, ETH Zentrum, CH-8092 Zürich, Switzerland. E-mail: ferretti@math.ethz.ch
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Abstract

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The purpose of this note is to present a somewhat unexpected relation between diophantine approximations and the geometric invariant theory. The link is given by Mumford's degree of contact. We show that destabilizing flags of Chow-unstable projective varieties provide systems of diophantine approximations which are better than those given by Schmidt's subspace theorem, and we give examples of these systems.

Keywords

diophantine approximationsgeometric invariant theorydegree of contactChow pointSegre classlocal ringsruled surfacesblow-upelliptic surfacesArakelov geometry
Type
Research Article
Information
Compositio Mathematica , Volume 121 , Issue 3 , May 2000 , pp. 247 - 262
Copyright
© 2000 Kluwer Academic Publishers