Secant Varieties and Successive Minima
نویسنده
چکیده
Let X be a semi-stable arithmetic surface over the spectrum S of the ring of integers in a number field K. We assume that the generic fiber XK is geometrically irreducible and has positive genus. Consider a line bundle L on X , which is non-negative on every vertical fiber and equipped with an admissible metric (in the sense of Arakelov [A]) of positive curvature. In [S] we have shown that any non-trivial extension class of L by the trivial line bundle is such that its L-norm is bounded away from zero.
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