M-REGULARITY OF Q-TWISTED SHEAVES AND ITS APPLICATION TO LINEAR SYSTEMS ON ABELIAN VARIETIES

Atsushi Ito

doi:10.1090/tran/8725

M-REGULARITY OF Q-TWISTED SHEAVES AND ITS APPLICATION TO LINEAR SYSTEMS ON ABELIAN VARIETIES

Atsushi Ito

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 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 Q-twisted sheaf implies property (Np) and jet-ampleness for ample line bundles on abelian varieties.

Original language	English
Pages (from-to)	6653-6673
Number of pages	21
Journal	Transactions of the American Mathematical Society
Volume	375
Issue number	9
DOIs	https://doi.org/10.1090/tran/8725
Publication status	Published - Sept 1 2022

Keywords

Abelian variety
linear system
M-regularity

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/tran/8725

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title = "M-REGULARITY OF Q-TWISTED SHEAVES AND ITS APPLICATION TO LINEAR SYSTEMS ON ABELIAN VARIETIES",

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 Q-twisted sheaves introduced by Z. Jiang and G. Pareschi [Ann. Sci. {\'E}c. Norm. Sup{\'e}r. (4) 53 (2020), pp. 815–846]. As an application, we show that the M-regularity of a suitable Q-twisted sheaf implies property (Np) and jet-ampleness for ample line bundles on abelian varieties.",

keywords = "Abelian variety, linear system, M-regularity",

author = "Atsushi Ito",

note = "Funding Information: Received by the editors December 1, 2021, and, in revised form, March 31, 2022. 2020 Mathematics Subject Classification. Primary 14C20, 14K99. Key words and phrases. Abelian variety, M-regularity, linear system. The author was supported by JSPS KAKENHI Grant Number 17K14162. Publisher Copyright: {\textcopyright} 2022 American Mathematical Society.",

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AU - Ito, Atsushi

N1 - Funding Information: Received by the editors December 1, 2021, and, in revised form, March 31, 2022. 2020 Mathematics Subject Classification. Primary 14C20, 14K99. Key words and phrases. Abelian variety, M-regularity, linear system. The author was supported by JSPS KAKENHI Grant Number 17K14162. Publisher Copyright: © 2022 American Mathematical Society.

PY - 2022/9/1

Y1 - 2022/9/1

N2 - 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 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 Q-twisted sheaf implies property (Np) and jet-ampleness for ample line bundles on abelian varieties.

AB - 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 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 Q-twisted sheaf implies property (Np) and jet-ampleness for ample line bundles on abelian varieties.

KW - Abelian variety

KW - linear system

KW - M-regularity

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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ER -

M-REGULARITY OF Q-TWISTED SHEAVES AND ITS APPLICATION TO LINEAR SYSTEMS ON ABELIAN VARIETIES

Abstract

Keywords

ASJC Scopus subject areas

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