## 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)