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

Thanks a lot.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Short exact sequence

Hi Bryan29

Welcom to the forum!

You might want to use

instead of $$.

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