3:30 pm, Seminar Hall
Fujita type conjectures for log-pluricanonical sheaves: a survey of available tools
Northwestern University, USA.
Fujita in 1988 conjectured that there is an effective bound on twists of ample line bundles to obtain global generation of canonical bundles. Since then similar conjectures in the relative setting has been proposed. Despite many important breakthroughs by Demailly, Reider, Ein, Lazarsfeld, Kawamata, Popa, Schnell et al., these conjectures remains unproved as of today. We will briefly walk through this history and focus on similar generation statements for the log-pluricanonical sheaves. We will discuss some of the algebraic techniques in use; weak positivity, to name a few, which can be seen both as a reason and a consequence of such generation problems.