Timeline for The Gysin map for a singular hypersurface
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 10, 2012 at 10:13 | comment | added | Alex Gavrilov | Perhaps, but I hope that the statement may be true as it is. I do not need the Whole Gysin sequence after all. | |
| Aug 10, 2012 at 8:02 | comment | added | Damian Rössler | When $Y$ is smooth, by Poincar\'e duality, the sequence you consider is the dual sequence of the sequence with compact supports $\dots H^{2n-i-2}_c(X\backslash Y,{\bf Q})\to H^{2n-i-2}(X,{\bf Q})\to H^{2n-i-2}(Y,{\bf Q})\to\dots$ This suggests that the "right sequence" without compact supports should be obtained by dualising the above sequence using Grothendieck-Verdier duality (which generalizes Poincar\'e duality to the non-smooth setting). In particular, you would expect the dualising complex to appear on $Y$ (and not just $\bf Q$). | |
| Aug 10, 2012 at 2:51 | comment | added | Alex Gavrilov | Thank you. Though I am not sure if it may be helpful. | |
| Aug 10, 2012 at 2:04 | comment | added | Charles Staats | If you work with Chow groups rather than cohomology, a version of this exact sequence is given (with much weaker hypotheses than the ones you have specified) in Fulton's Intersection Theory, Proposition 1.8, page 21. This is not quite what you are asking for, but it suggests that something similar is probably true for cohomology. | |
| Aug 9, 2012 at 10:05 | history | asked | Alex Gavrilov | CC BY-SA 3.0 |