Welcom to the forum!

You might want to use

`[math][/math]`

instead of $$.

]]>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.

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