18.727 Topics in Algebraic Geometry

Positivity in Algebraic Geometry, M 4-5:30 Room 2-143, W 4:15-5:45 Room 2-255

NOTE THAT THERE HAS BEEN A ROOM CHANGE FOR MONDAYS!!! FROM NOW ON THE CLASS WILL BE IN ROOM 2-143 ON MONDAYS. ON WEDNESDAYS THE ROOM STAYS THE SAME.

NEW TIME: In order to avoid conflict with Prof. Mrowka's course and the Harvard Number Theory seminar, this course has been moved to M 4-5:30 and W 4:15-5:45

Announcements: There will be no class on Wednesday December 6 or Monday December 11.

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, coskun@math.mit.edu

Office: 2-167

Text: Lazarsfeld, R. Positivity in Algebraic Geometry Vol I and II, Springer, 2004.

Handouts: Syllabus(pdf)