M-regularity of ℚ-twisted sheaves and its application to linear systems on abelian varieties
Atsushi Ito
Source 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 \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 Q \mathbb {Q} -twisted sheaf implies property ( N p ) (N_p) and jet-ampleness for ample line bundles on abelian varieties.
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