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arXiv · 1806.05087

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

Jie Liu
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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 $\varepsilon(X,-K_X;x)\leq 1$ for all points $x\in X$ if and only if $\vert-K_X\vert$ is not base point free.

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Jie Liu. 2018-06-13. Seshadri constants of the anticanonical divisors of Fano manifolds with large index. https://arxiv.org/abs/1806.05087

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