Lower bounds for Seshadri constants via successive minima of line bundles

Ballaÿ, François

doi:10.1090/proc/16514

Lower bounds for Seshadri constants via successive minima of line bundles
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by François Ballaÿ

Proc. Amer. Math. Soc. 151 (2023), 4653-4660

DOI: https://doi.org/10.1090/proc/16514

Published electronically: August 4, 2023

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Abstract:

Given a nef and big line bundle $L$ on a projective variety $X$ of dimension $d \geq 2$, we prove that the Seshadri constant of $L$ at a very general point is larger than $(d+1)^{\frac {1}{d}-1}$. This slightly improves the lower bound $1/d$ established by Ein, Küchle and Lazarsfeld [J. Differential Geom. 42 (1995), pp. 193–219]. The proof relies on the concept of successive minima for line bundles recently introduced by Ambro and Ito [Adv. Math. 365 (2020), 38 pp.].

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