Timeline for Group of Hodge classes
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26, 2013 at 15:11 | vote | accept | Bryan261 | ||
| Nov 26, 2013 at 15:05 | answer | added | Dan Petersen | timeline score: 3 | |
| Nov 26, 2013 at 13:16 | review | Close votes | |||
| Nov 26, 2013 at 14:35 | |||||
| Nov 26, 2013 at 13:06 | comment | added | Bryan261 | I'm from a foreign country, i don't speak well engish. sorry .. $ X $ and $ Y $ are subvarieties of a smooth projective variety $ M $ such that $ M = X \bigcup Y $. I would like to know if we can construct a short exact sequence $ 0 \to \mathrm{Hdg} ( X \bigcup Y ) \to \mathrm{Hdg} ( X ) \oplus \mathrm{Hdg} ( Y ) \to \mathrm{Hdg} ( X \bigcap Y )$. Thanks a lot. | |
| Nov 26, 2013 at 12:59 | comment | added | Dan Petersen | I voted to close as "unclear" - I don't think the question makes any sense as written. Are $X$ and $Y$ subvarieties of some other variety? Open or closed? Constructible? | |
| Nov 26, 2013 at 12:55 | comment | added | jmc | Actually, it is not so clear to me what you want with this question. Could you sketch more context? For example, do you consider my previous comment trivial, or is that the sort of thing you are looking for. If you think it is trivial, then maybe you can include it as a sort of context/introduction in your question. | |
| Nov 26, 2013 at 12:54 | comment | added | jmc | If $f \colon X \to Y$ is a morphism of smooth projective varieties, then the induced map $f^{*} \colon H(Y, \mathbb{Q}) \to H(X, \mathbb{Q})$ is a morphism of Hodge structures. So $H^{2k}(Y, \mathbb{Q})$ mapst to $H^{2k}(X, \mathbb{Q})$, and $H^{k,k}(Y)$ maps to $H^{k,k}(X)$. Therefore, there is an induced map $f^{*} \colon \textrm{Hdg}_{k}(Y) \to \textrm{Hdg}_{k}(X)$. | |
| Nov 26, 2013 at 12:46 | review | First posts | |||
| Nov 26, 2013 at 12:47 | |||||
| Nov 26, 2013 at 12:27 | history | asked | Bryan261 | CC BY-SA 3.0 |