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Charles Staats
Charles Staats
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Let $\pi:X\rightarrow Y$ be a double cover of complex varieties and take $L$ holomorphic line bundle on $Y$.

I read that there are the isomorphisms

  1. $H^p(X,\mathcal{O}_X)\simeq H^p(Y,\pi_*\mathcal{O}_Y)$$H^p(X,\mathcal{O}_X)\simeq H^p(Y,\pi_*\mathcal{O}_X)$

  2. $H^p(Y,\mathcal{O}_Y\oplus L)\simeq H^p(Y,\mathcal{O}_Y)\oplus H^p(Y,L)$

How can i prove them?

Let $\pi:X\rightarrow Y$ be a double cover of complex varieties and take $L$ holomorphic line bundle on $Y$.

I read that there are the isomorphisms

  1. $H^p(X,\mathcal{O}_X)\simeq H^p(Y,\pi_*\mathcal{O}_Y)$

  2. $H^p(Y,\mathcal{O}_Y\oplus L)\simeq H^p(Y,\mathcal{O}_Y)\oplus H^p(Y,L)$

How can i prove them?

Let $\pi:X\rightarrow Y$ be a double cover of complex varieties and take $L$ holomorphic line bundle on $Y$.

I read that there are the isomorphisms

  1. $H^p(X,\mathcal{O}_X)\simeq H^p(Y,\pi_*\mathcal{O}_X)$

  2. $H^p(Y,\mathcal{O}_Y\oplus L)\simeq H^p(Y,\mathcal{O}_Y)\oplus H^p(Y,L)$

How can i prove them?

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Tom Fellmann
Tom Fellmann
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Sheaf cohomology and double covers

Let $\pi:X\rightarrow Y$ be a double cover of complex varieties and take $L$ holomorphic line bundle on $Y$.

I read that there are the isomorphisms

  1. $H^p(X,\mathcal{O}_X)\simeq H^p(Y,\pi_*\mathcal{O}_Y)$

  2. $H^p(Y,\mathcal{O}_Y\oplus L)\simeq H^p(Y,\mathcal{O}_Y)\oplus H^p(Y,L)$

How can i prove them?