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Mumford's Degree of Contact and Diophantine Approximations

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Compositio Mathematica

Abstract

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.

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Authors and Affiliations

  1. Departement Mathematik, ETH Zentrum, CH-8092, Zürich, Switzerland

    Roberto G. Ferretti

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  1. Roberto G. Ferretti
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Ferretti, R.G. Mumford's Degree of Contact and Diophantine Approximations. Compositio Mathematica 121, 247–262 (2000). https://doi.org/10.1023/A:1001726515286

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  • DOI: https://doi.org/10.1023/A:1001726515286

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