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Aug 5, 2022 at 11:46 vote accept TCiur
Aug 1, 2022 at 15:45 answer added Will Sawin timeline score: 2
Aug 1, 2022 at 10:16 comment added TCiur @WillSawin How would one produce an upper bound of $4$ in characteristic $2$? I think that would be enough to solve all my problems. In this case it doesn't hold that $\pi_*\pi^*H = H + H(\eta)$
Jul 27, 2022 at 12:11 comment added TCiur @abx I edited the question. I am interested in the case where $\pi$ comes from a conic bundle structure on a cubic threefold. I would probably have to use the geometry of the cubic threefold then.
Jul 27, 2022 at 12:08 history edited TCiur CC BY-SA 4.0
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Jul 27, 2022 at 11:47 comment added Will Sawin It seems likely that the possible values in characteristic $2$ are also $3$ or $4$, with $3$ generic.
Jul 26, 2022 at 18:37 comment added abx Even in characteristic 0, $h^0(M)$ depends on the choice of $\pi$ — it can be 3 or 4.
Jul 26, 2022 at 17:29 history asked TCiur CC BY-SA 4.0