Abstract
Let X be an arithmetic surface, and let L be a line bundle on X. Choose a metric h on the lattice Λ of sections of L over X. When the degree of the generic fiber of X is large enough, we get lower bounds for the successive minima of (Λ,h) in terms of the normalized height of X. The proof uses an effective version (due to C. Voisin) of a theorem of Segre on linear projections and Morrison’s proof that smooth projective curves of high degree are Chow semistable.
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