Seshadri constants of the anticanonical divisors of Fano manifolds with large index

2018/06/13 by Liu, Jie
#14C20 (Primary) #14J30 #14J45 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.05087

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,-K_X;x)≤ 1 for all points x∈ X if and only if \vert-K_X\vert is not base point free.

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