Lengths of periods and seshadri constants of abelian varieties

Abstract

We start by recalling the definition of Seshadri constants. Let X be a smooth complex projective variety, let L be an ample line bundle on X , and fix a point x ∈ X . Consider the blowing-up f : Y = Blx(X) −→ X of X at x, with exceptional divisor E = f(x) ⊂ Y . Then for 0 < ǫ ≪ 1 the cohomology class fc1(L)− ǫ · [E] will lie in the Kahler cone of Y . As a measure of how positive L is locally near x we ask in effect how large we can take ǫ to be while keeping the class in question positive. More precisely, set