Timeline for How does the MHS on $H_Y^i(X)$ behave with respect to the Thom isomorphism?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Nov 13, 2020 at 9:14 | vote | accept | user2520938 | ||
| Nov 13, 2020 at 8:51 | answer | added | Dan Petersen | timeline score: 4 | |
| Nov 13, 2020 at 4:37 | comment | added | AG learner | In Akira Fujiki's Duality of Mixed Hodge Structures of Algebraic Varieties, it is proved that there is a natural perfect pairing $H^i_Y(Y,\mathbb Q)\times H^{2n-i}(Y,\mathbb Q)\to \mathbb Q$ which induces duality of mixed $\mathbb Q$-Hodge structures. Together with the standard pairing $H^{i-2c}(Y,\mathbb Q)\times H^{2n-i}(Y,\mathbb Q)\to \mathbb Q$, the isomorphism $H^i_Y(X)\cong H^{i-2c}(Y)$ preserves mixed Hodge structures. This should be compatible with Thom isomorphism. | |
| Nov 12, 2020 at 21:20 | history | asked | user2520938 | CC BY-SA 4.0 |