Yes, $ X $ and $ Y $ are closed. Thank you.

Thank you very much. :-) $ \\ $ Can you tell me, please, in which books can i find somethings about this subject ? Thank you.

I'm sorry, can I formulate my question differently ?! sorry, because i need to have $ \mathrm{Hdg}_k ( X ) \oplus \mathrm{Hdg}_k ( Y ) \to \mathrm{Hdg}_k ( X \bigcup Y ) $ surjective. In other words : do we have $ \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 $ a exact sequence ? Thanks a lot.

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.