# A recent talk by Kollar on cohomology of structure sheaves

Recently I noticed an intriguing talk by Kollár at the MAGIC conference. The abstract says:

Title: Cohomology groups of structure sheaves

Abstract: I will discuss the behavior of cohomology groups of the structure sheaf and of the dualizing sheaf under deformations and birational maps.

This sounds very interesting to me and can be potentially helpful for my research. However, I could not find any further information about the talk, except for some pictures, from which I shamefully failed to reconstruct the materials!

Would any expert who happened to be there please point me to some references for which the talk is based on, or better yet, explain briefly the motivations and key results? Many thanks.

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## 1 Answer

I would guess, he was lecturing about this article: http://arxiv.org/abs/0902.0648

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Or rather, section 7 of that paper of Koll\'ar and Kov\'acs. You can also look at an old paper of Steenbrink: "Cohomologically insignificant degenerations". It has some of the basic ideas at least for deformations, that began some of this. –  Karl Schwede Jun 9 '10 at 8:29
In a talk he gave with the same title at Princeton a month ago, he also talked about the results/techniques of arxiv.org/abs/0911.3599. –  Bhargav Jun 9 '10 at 13:39
Great! Thanks a lot, guys! –  Hailong Dao Jun 9 '10 at 22:16