How to prove that the singular cohomology of $X=V(xy-zw)\setminus 0 \subset \mathbb{C}^4$ is $$H^*(X,\mathbb{Z})=\{\mathbb{Z},0,\mathbb{Z},\mathbb{Z},0,\mathbb{Z}\}?$$ Preferably, I would like to know whether the stronger result $$X \simeq S^2 \times S^3$$ holds?
2026-04-01 14:43:32.1775054612
Cohomology of quadric in $\mathbb{C}^4$ at infinity
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