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.].References
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Bibliographic Information
- François Ballaÿ
- Affiliation: Normandie Univ, UNICAEN, CNRS, LMNO, 14000 Caen, France
- Email: francois.ballay@unicaen.fr
- Received by editor(s): November 6, 2022
- Received by editor(s) in revised form: March 15, 2023, and April 15, 2023
- Published electronically: August 4, 2023
- Communicated by: Rachel Pries
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 4653-4660
- MSC (2020): Primary 14C20
- DOI: https://doi.org/10.1090/proc/16514
- MathSciNet review: 4634871