M-regularity of $\mathbb {Q}$-twisted sheaves and its application to linear systems on abelian varieties
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Abstract:
G. Pareschi and M. Popa [J. Amer.Math. Soc. 16 (2003), pp. 285–302] give criterions for global generation and surjectivity of multiplication maps of global sections of coherent sheaves on abelian varieties in the theory of M-regularity. In this paper, we refine some of their criterions via the M-regularity of $\mathbb {Q}$-twisted sheaves introduced by Z. Jiang and G. Pareschi [Ann. Sci. Éc. Norm. Supér. (4) 53 (2020), pp. 815–846]. As an application, we show that the M-regularity of a suitable $\mathbb {Q}$-twisted sheaf implies property $(N_p)$ and jet-ampleness for ample line bundles on abelian varieties.References
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Additional Information
- Atsushi Ito
- Affiliation: Department of Mathematics, Faculty of Natural Science and Technology, Okayama University, Okayama, Japan
- MR Author ID: 1019212
- Email: ito-atsushi@okayama-u.ac.jp
- Received by editor(s): December 1, 2021
- Received by editor(s) in revised form: March 31, 2022
- Published electronically: June 30, 2022
- Additional Notes: The author was supported by JSPS KAKENHI Grant Number 17K14162
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 6653-6673
- MSC (2020): Primary 14C20, 14K99
- DOI: https://doi.org/10.1090/tran/8725
- MathSciNet review: 4474904