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**Bryan29****Guest**

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.

Can you tell me if you know some references about this subject?

Thanks a lot.

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

Hi Bryan29

Welcom to the forum!

You might want to use

`[math][/math]`

instead of $$.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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