Timeline for Can Enriques Surfaces have non-trivial TWISTED Fourier-Mukai partners?
Current License: CC BY-SA 3.0
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| Feb 20, 2015 at 13:42 | comment | added | Tony Pantev | My guess is that it will be impossible to do it with a genuine surface. One might be able to check this directly by looking at the classification of surfaces, listing all possible twisted Hodge structures, and then checking that the required lattice $E_{8}(-2)\oplus H(2)\oplus H$ can never appear in a twist of a surface. I have not done this carefully but it seems doable. You basically have to rule out K#s and rational elliptic surfaces. | |
| Feb 19, 2015 at 15:01 | comment | added | HNuer | Thanks Tony, I agree this is very natural. Is this the only thing that can happen though? Is there something that rules this out when X is a genuine smooth projective surface? | |
| Feb 19, 2015 at 14:35 | history | answered | Tony Pantev | CC BY-SA 3.0 |