Abstract
Seshadri constants, introduced by Demailly, measure the local positivity of a nef divisor at a point. In this paper, we compute the Seshadri constants of the anticanonical divisors of Fano manifolds with coindex at most 3 at a very general point. As a consequence, if X is a nonsingular Fano threefold which is very general in its deformation family, then ε(X,−KX;x)≤1 for all points x∈X if and only if |−KX| is not base point free.
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