Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Does there exist a smooth, projective, complex algebraic varietiyvariety$X$, with two cohomology classes $\alpha,\beta \in H^{*}(X,\mathbb{Z})$ neither $\alpha$ nor $\beta$ is torsion but the product $\alpha \cup \beta$ is non-trivial and torsion?
Does there exist a smooth, projective, complex algebraic varietiy$X$, with two cohomology classes $\alpha,\beta \in H^{*}(X,\mathbb{Z})$ neither $\alpha$ nor $\beta$ is torsion but the product $\alpha \cup \beta$ is non-trivial and torsion?
Does there exist a smooth, projective, complex algebraic variety$X$, with two cohomology classes $\alpha,\beta \in H^{*}(X,\mathbb{Z})$ neither $\alpha$ nor $\beta$ is torsion but the product $\alpha \cup \beta$ is non-trivial and torsion?
Algebraic varieties with certain topological properties
Does there exist a smooth, projective, complex algebraic varietiy $X$, with two cohomology classes $\alpha,\beta \in H^{*}(X,\mathbb{Z})$ neither $\alpha$ nor $\beta$ is torsion but the product $\alpha \cup \beta$ is non-trivial and torsion?
