Meeting with Kenji Matsuki
This is the regular meeting with Prof. Matsuki at Purdue discussing current trend in birational geometry.
-September 7rd, 2012: Main Theorem of [BCHM]: Existence of MM or MFS for (X,\Delta): projective, klt, \QQ-factorial, with $\Delta a big divisor.
Theorem A: Existence of pl-flips. Next time show how existence of pl-flips implies existence of klt-flips.
-August 24th, 2012: I would love to collect interesting questions and open problems in birational geometry for future study. Also, there are several interesting and significant papers to study. We shall make a brief list.
- Next week: Present my prove of almost positivity of direct images of pluricanonical sheaves. Also give a comparison of KVT, Kollar's vanishing, and Bogomolov-Sommese vanishing.
- Review of the minimal model program and BCHM.
- Known and unknown in the minimal model program.
- Go through Cascini-Lazic's proof of finite generation of canonical rings. It seems they only use Kawamata Viehweg vanishing theorem but without multiplier ideal sheaves.
Copyright © 2012. All Rights Reserved.