The mini-course on Day 1~4 is given by Prof. Osamu Fujino (Kyoto University). 

The venue of the mini-course is Building 129, Room 406 on the 4th floor (상산수리과학관). 

Title: Minimal model theory for projective morphisms between complex analytic spaces

Day 1: June 29 (Mon)  Lecture : 15:00-17:00

Day 2: June 30 (Tue)  Lecture : 15:00-17:00

Day 3: July 01 (Wed)  Lecture : 10:30-12:30

Day 4: July 02 (Thur) Lecture : 10:30-12:30

Abstract:

This mini-course introduces minimal model theory for projective morphisms between complex analytic spaces.

Day 1.

We begin with a review of the classical minimal model theory for algebraic varieties. We then explain how its main ideas and results can be extended to projective morphisms between complex analytic spaces.

Day 2.

We discuss the foundations of complex analytic spaces, including Stein spaces and Stein compact subsets. We also introduce basic notions related to projective morphisms and relatively ample line bundles, which play essential roles in the minimal model program.

Day 3.

We study the Kleiman--Mori cone, Kleiman’s ampleness criterion, and related topics in the complex analytic setting. We also explain Nakayama’s finiteness theorem, which plays a crucial role in the development of minimal model theory in this setting.

Day 4.

On the final day, we discuss several advanced topics. One possible topic is the canonical bundle formula in the complex analytic setting, a result established recently by Kenta Hashizume. Depending on the audience and available time, we may also touch on related developments and applications.

https://sites.google.com/view/snu-mmp