Finite generation of the canonical ring after Lazic

27 November 2009
Professor Alessio Corti
A key birational invariant of a compact complex manifold is its "canonical ring." The ring of modular forms in one or more variables is an example of a canonical ring. Recent developments in higher dimensional algebraic geometry imply that the canonical ring is always finitely generated:this is a long-awaited major foundational result in algebraic geometry. In this talk I define all the terms and discuss the result, some applications, and a recent remarkable direct proof by Lazic.