Linear systems on abelian varieties via M-regularity of Q-twisted sheaves

Abstract: For an ample line bundle $L$ on an abelian variety $X$, it is known that $L^n$ is basepoint free if $n \geq 2$, projectively normal if $n \geq 3$, and the ideal of $X$ embedded by $|L^n|$ is generated by quadrics if $n \geq 4$. As a generalization of these results, Lazarsfeld conjectures that $L^n$ satisfies property $(N_p)$ if $n \geq p+3$. This conjecture is affirmatively proved by Pareschi and strengthen by Pareschi-Popa by the theory of M-regularity. Recently, Jiang and Pareschi consider (variants of) M-regularity of $\mathbb{Q}$-twisted sheaves and it turns out that this is very useful when we study the linear system $|L|$ of $L$ itself, not only $L^n$ for $n \geq 2$. In this talk, I will explain this topic and some recent results.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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