BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Atsushi Ito (Nagoya University) DTSTART:20210225T100000Z DTEND:20210225T110000Z DTSTAMP:20260423T021354Z UID:ZAG/98 DESCRIPTION:Title: Lin ear systems on abelian varieties via M-regularity of Q-twisted sheaves \nby Atsushi Ito (Nagoya University) as part of ZAG (Zoom Algebraic Geomet ry) seminar\n\n\nAbstract\nFor an ample line bundle $L$ on an abelian vari ety $X$\, it is known that $L^n$ is basepoint free if $n \\geq 2$\, projec tively 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 result s\, Lazarsfeld conjectures that $L^n$ satisfies property $(N_p)$ if $n \\g eq p+3$.\nThis conjecture is affirmatively proved by Pareschi and strength en by Pareschi-Popa by the theory of M-regularity. Recently\, Jiang and Pa reschi consider (variants of) M-regularity of $\\mathbb{Q}$-twisted sheave s and it turns out that this is very useful when we study the linear syste m $|L|$ of $L$ itself\, not only $L^n$ for $n \\geq 2$. In this talk\, I w ill explain this topic and some recent results.\n LOCATION:https://researchseminars.org/talk/ZAG/98/ END:VEVENT END:VCALENDAR