Timeline for Globalization of Brieskorn-Grothendieck resolution
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 23, 2020 at 14:47 | comment | added | AG learner | Dear @Balazs, here is an update of the research on this problem. In the two references you mentioned, there are relevant theorems, e.g., Kollár and Mori, Thm 4.43, Kollár and Shepherd-Barron, Thm 2.4. However, these theorems are about local deformations, i.e., the base is not global. We also consulted Kollar, and he thinks the answer is negative: "the simultaneous resolution exists locally analytically, so when we glue then we get something that is not projective, no matter what base change you do..." But he mentioned there will be a stack represent simultaneous resolution, but not separated. | |
| Mar 18, 2020 at 5:55 | comment | added | AG learner | Dear @Balazs: Thank you very much for the suggested reference. I was not aware of this development after Brieskorn. If I understand correctly, "simultaneous resolution" as I defined above is the same as "very weak simultaneous resolution" in Kollár and Shepherd-Barron, and according to Theorem 2.4 (due to Laufer) in the paper, the answer to my question is yes because $K^2_{rel}$ is locally constant. Am I right? | |
| Mar 16, 2020 at 10:35 | comment | added | Balazs | Look in Kollár and Shepherd-Barron, Threefolds and deformations of surface singularties, Inventiones 1988, Section 2, or Kollár and Mori, Birational geometry of algebraic varieties, CUP 1998, Section 4.3. I am sure there are other sources; these are the ones I have at hand. | |
| Mar 15, 2020 at 18:06 | history | edited | AG learner | CC BY-SA 4.0 |
typo correction, add an example
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| Mar 15, 2020 at 5:47 | history | asked | AG learner | CC BY-SA 4.0 |