Timeline for What can be said about a projective morphisms that admit decomposition theorem like smooth morphisms?
Current License: CC BY-SA 4.0
9 events
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| Oct 11, 2020 at 21:16 | history | edited | Donu Arapura | CC BY-SA 4.0 |
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| Sep 3, 2020 at 7:11 | comment | added | guest0803 | @Chris That is unfortunately not correct. Blow-ups already give you examples where discriminant is not of pure codim 1. | |
| Sep 2, 2020 at 11:41 | history | edited | Donu Arapura | CC BY-SA 4.0 |
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| Sep 2, 2020 at 6:56 | comment | added | Chris | Isn't the discriminant always of pure codimension one (if non-empty)? | |
| Sep 1, 2020 at 21:41 | vote | accept | guest0803 | ||
| Sep 6, 2020 at 14:42 | |||||
| Sep 1, 2020 at 21:33 | comment | added | guest0803 | Thanks! I will look forward to it. Somehow I have the feeling that such $f$ (additional assumption inclusive) cannot have divisorial discriminant locus. But I don't have an argument or a counter-example. | |
| Sep 1, 2020 at 21:10 | comment | added | Donu Arapura | You're welcome. OK, with added assumptions about direct images, I agree that the local monodromy is trivial. Surprisingly, this is not enough to guarantee smoothness. I'll expand my answer later. | |
| Sep 1, 2020 at 20:48 | comment | added | guest0803 | Dear Prof. Arapura, thanks so much for the beautiful answer. And of course, I meant to also add that $R^if_*\mathbb{C}$ are all local systems (if I understand correctly the comment about local monodromy is true in this case.). Under this additional assumption, can one conclude smoothness of $f$? Since the answer is really helpful and explicit, I will leave the question as it is and add the part about the local system assumption at the end. | |
| Sep 1, 2020 at 16:54 | history | answered | Donu Arapura | CC BY-SA 4.0 |