How do we compute the even cohomology $H^2i(Q)$ of the affine hyperquadric?

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How do we compute the even cohomology $H^2i(Q)$ of the affine hyperquadric $Q:=biggl(z_1,...,z_n+1)inmathbbC^n+1biggl$? Furthermore, what is the curvature form $Omega$ on $Q$, i.e. what is a reasonable Kähler metric?



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    How do we compute the even cohomology $H^2i(Q)$ of the affine hyperquadric $Q:=biggl(z_1,...,z_n+1)inmathbbC^n+1biggl$? Furthermore, what is the curvature form $Omega$ on $Q$, i.e. what is a reasonable Kähler metric?



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    homology-cohomology affine-geometry




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      How do we compute the even cohomology $H^2i(Q)$ of the affine hyperquadric $Q:=biggl(z_1,...,z_n+1)inmathbbC^n+1biggl$? Furthermore, what is the curvature form $Omega$ on $Q$, i.e. what is a reasonable Kähler metric?



      Thanks!




      homology-cohomology affine-geometry




      share|cite|improve this question













      How do we compute the even cohomology $H^2i(Q)$ of the affine hyperquadric $Q:=biggl(z_1,...,z_n+1)inmathbbC^n+1biggl$? Furthermore, what is the curvature form $Omega$ on $Q$, i.e. what is a reasonable Kähler metric?



      Thanks!





      homology-cohomology affine-geometry





      share|cite|improve this question












      share|cite|improve this question




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