Welcome to 18.727! This course intends to bridge the gap between introductory courses in algebraic geometry and current research in higher dimensional complex algebraic geometry. We will develop tools such as big and nef line bundles, vanishing theorems and multiplier ideals in order to understand the geometry of higher dimensional varieties. The focus of the course will be on concrete examples and applications. We will end the course by discussing current developments such as Siu's theorem on the invariance of plurigenera and Boucksom, Demailly, Paun and Peternell's characterization of uniruled varieties. If time permits, we will discuss recent progress in the Minimal Model Program. The main text for the course will be Rob Lazarsfeld's volumes Positivity in Algebraic Geometry.
Prerequisites: An introductory course in complex or algebraic geometry. Either of the following is ample preparation for the course: A first year graduate class in algebraic geometry at the level of Chapters 2 and 3 of Hartshorne or a first year graduate class in complex geometry at the level of Chapters 0 and 1 of Griffiths and Harris.
Lecturer: Izzet Coskun, email@example.com
Text: Lazarsfeld, R. Positivity in Algebraic Geometry Vol I and II, Springer, 2004.