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Zhiwei Zheng
Zhiwei Zheng
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Take $X$ a hypersurface in $\mathbb{C}P^{n+1}$ of degree $d$, denote $\Lambda_X=H^n(X,\mathbb{Z})$. We know that $\Lambda_X$ is a finitely generated Abelian group. I was wondering whether $\Lambda_X$ is always free (for any $n$, $d$). Anyone know an answer or a refrence aboutof this? Thanks a lot!

Take $X$ a hypersurface in $\mathbb{C}P^{n+1}$ of degree $d$, denote $\Lambda_X=H^n(X,\mathbb{Z})$. We know that $\Lambda_X$ is a finitely generated Abelian group. I was wondering whether $\Lambda_X$ is always free (for any $n$, $d$). Anyone know an answer or a refrence about this? Thanks a lot!

Take $X$ a hypersurface in $\mathbb{C}P^{n+1}$ of degree $d$, denote $\Lambda_X=H^n(X,\mathbb{Z})$. We know that $\Lambda_X$ is a finitely generated Abelian group. I was wondering whether $\Lambda_X$ is always free (for any $n$, $d$). Anyone know an answer or a refrence of this? Thanks a lot!

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Zhiwei Zheng
Zhiwei Zheng
  • 337
  • 1
  • 11

Freeness of the integral middle cohomology of a smooth hypersurface in $\mathbb{C}P^{n+1}$

Take $X$ a hypersurface in $\mathbb{C}P^{n+1}$ of degree $d$, denote $\Lambda_X=H^n(X,\mathbb{Z})$. We know that $\Lambda_X$ is a finitely generated Abelian group. I was wondering whether $\Lambda_X$ is always free (for any $n$, $d$). Anyone know an answer or a refrence about this? Thanks a lot!