Timeline for Example of projective, $ F $-regular variety $ X $ and smooth sub-variety $ Y $ such that $ \operatorname{Bl}_{Y}(X) $ is not $ F $-regular?
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| Jan 26, 2023 at 4:17 | comment | added | Schemer1 | I made edits to the argument because I really want to understand what the error in my thought process was. If $ S_{1} \cong S $ and $ R \subseteq S $ is a split inclusion and $ S_{1} $ is $ F $-regular, then is $ R $ still $ F $-regular? I ask because my mistake may have been in understanding the importance of the term "split inclusion". In this argument I did not have a split inclusion, but the weaker condition above. Thank you again @KarlSchwede as you have been valuable in helping me further my understanding of the theory that you, Karen Smith and others have developed. | |
| Jan 26, 2023 at 4:11 | history | edited | Schemer1 | CC BY-SA 4.0 |
added 40 characters in body
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| Jan 25, 2023 at 17:08 | comment | added | Karl Schwede | There are many such examples. If $X$ is globally $F$-regular, then $-K_X$ is big (see my paper with Karen Smith on globally $F$-regular varieties). Take $\mathbb{P}^2$ and blow up 9 points. Then $-K_X$ is not big. I think this example is in the paper I mentioned above. I also do not understand your argument, I don't see the split inclusion. | |
| Jan 22, 2023 at 9:12 | history | asked | Schemer1 | CC BY-SA 4.0 |