Comptes Rendus
Article de recherche - Géométrie algébrique
A remark on the effective nonvanishing of Calabi–Yau varieties
[Une remarque sur la non-annulation effective des variétés de Calabi–Yau]
Yiming Zhu1
1 Department of Mathematics, Southern University of Science and Technology, 1088 Xueyuan Rd, Shenzhen 518055, China
Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1059-1063

For a Calabi–Yau variety $X$, we prove that there exists a positive integer $m$, depending on two natural invariants of the fiber of its Albanese map, such that the pluricanonical system $\vert mK_X \vert $ is non-empty.

Pour une variété de Calabi–Yau $X$, nous démontrons qu’il existe un entier strictement positif $m$, dépendant de deux invariants naturels de la fibre de son application d’Albanese, tel que le système pluricanonique $\vert mK_X \vert $ soit non vide.

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DOI : 10.5802/crmath.735
Classification : 14E05

Yiming Zhu 1

1 Department of Mathematics, Southern University of Science and Technology, 1088 Xueyuan Rd, Shenzhen 518055, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A remark on the effective nonvanishing of {Calabi{\textendash}Yau} varieties},
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     pages = {1059--1063},
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     volume = {363},
     doi = {10.5802/crmath.735},
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Yiming Zhu. A remark on the effective nonvanishing of Calabi–Yau varieties. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1059-1063. doi: 10.5802/crmath.735

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