Timeline for Deformation equivalent Hodge structures
Current License: CC BY-SA 4.0
5 events
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| Oct 8, 2020 at 15:26 | comment | added | Kevin Casto | Ah, I see, so what you would need is that any pair of Kahler manifolds homotopic to the Catanese-Manetti example (where the homotopies respects the Hodge structures) are necessarily not deformation equivalent. Is that right? In any case, perhaps you should look at their paper and see if you can make that work, since it's close to what you want. | |
| Oct 8, 2020 at 15:12 | comment | added | user164740 | We are asking if the oriented homotopy types together with the Hodge structures have Kähler representatives that are deformation equivalent. The absence of such representatives in your example is not clear to me. For instance there could be an oriented homeomorphism between the surfaces respecting the Hodge structures. Say, if the off-diagonal Hodge numbers vanish any homeomorphism must respect the Hodge structures. | |
| Oct 8, 2020 at 15:07 | comment | added | Kevin Casto | Your question seems to be asking if two Kahler manifolds that are (oriented) homotopy equivalent and have the same Hodge numbers are deformation equivalent. Catanese and Manetti gave an example of two oriented diffeomorphic but not deformation equivalent smooth projective surfaces. Since Hodge numbers are topological invariants of surfaces, these two must have the same Hodge numbers. | |
| Oct 8, 2020 at 11:23 | comment | added | user164740 | My apologies, I am unable to follow the logic of this answer. | |
| Oct 8, 2020 at 11:00 | history | answered | Kevin Casto | CC BY-SA 4.0 |