|Speaker:||Shinnosuke Okawa (Osaka U)|
|Title:||Non-existence of semi-orthogonal decompositions and sections of the canonical bundle|
|Date (JST):||Mon, Nov 25, 2013, 14:00 - 17:00|
|Place:||Seminar Room A|
It is expected, and has been partially verified, that steps of MMP for a smooth projective variety correspond to SODs (semi-orthogonal decompositions) of its derived category of coherent sheaves. On the other hand, derived categories of some minimal varieties also admit SODs. In this sense SODs are finer than MMP.
In this talk I will explain an attempt to show that minimal varieties with non-trivial SODs are `rare', with an emphasis
on the case of surfaces. For this I will show several constraints which should be fulfilled by arbitrary SODs, and explain that under certain conditions they lead to the non-existence of SODs.
I will present the results obtained so far in the first part of the talk, and the details of the proof and remaining problems will be discussed in the second part.
Whole talk is based on a joint work with Kotaro Kawatani.
|Remarks:||14:00-15:00 (Part I)
15:30-17:00 (Part II)