M-regularity of $\mathbb{Q}$-twisted sheaves and its application to linear systems on abelian varieties

TL;DR

This paper extends the concept of M-regularity to $Q$-twisted sheaves on abelian varieties and demonstrates its implications for properties like property $(N_p)$ and jet-ampleness of line bundles.

Contribution

It generalizes existing criteria for M-regularity to $Q$-twisted sheaves and applies this to derive new results on line bundle properties on abelian varieties.

Findings

M-regularity of $Q$-twisted sheaves implies property $(N_p)$

M-regularity leads to jet-ampleness of line bundles

Generalization of criteria for global generation and surjectivity

Abstract

G. Pareschi and M. Popa give criterions for global generations and surjectivity of multiplication maps of global sections of coherent sheaves on abelian varieties in the theory of M-regularity. In this paper, we generalize some of their criterions via the M-regularity of $\mathbb{Q}$-twisted sheaves. 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.