Algebraic Geometry Seminar: On Fujita Type Conjectures

Abstract:  One of the most natural questions in algebraic geometry is whether there is an effective bound on twists of ample line bundles to obtain global generation of coherent sheaves. Fujita in 1988 conjectured that the bound for the canonical bundle depends only on the dimension of the variety. Despite many important breakthroughs by Reider, Ein, Lazarsfels, Kawamata et al., the conjecture remains unproved as of today. We will walk through this history and discuss some recent developments on a relative analog of Fujita's conjecture.

Host: Patricio Gallardo