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## #1 2013-11-29 08:14:15

Bryan29
Guest

### Short exact sequence

I'm from a foreign country, I don't speak well English. Sorry.

My question is :
$X$ 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 $$\mathrm{Hdg}_k ( X \bigcap Y ) \to \mathrm{Hdg}_k ( X ) \oplus \mathrm{Hdg}_k ( Y ) \to \mathrm{Hdg}_k ( X \bigcup Y ) \to 0$$ such that $\mathrm{Hdg}_k ( X ) = H^{k,k} ( X ) \bigcap H^{2k} ( X , \mathbb{Q} )$ is the group of Hodge classes.

Thanks a lot.

## #2 2013-11-29 15:32:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,919

### Re: Short exact sequence

Hi Bryan29

Welcom to the forum!

You might want to use



instead of .

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