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

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 $\epsilon (X,-K_X;x)\le 1$ for all points $x\in X$ if and only if $|-K_X|$ is not base point free.

Totally rewritten, but the results remain unchanged

References in corpus (1)

• Existence of good divisors on Mukai varieties