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Francesco Polizzi
Francesco Polizzi
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(1,1)-form doesn`tthat does not come from a divisor

Let $M$ be projective complex manifold. The Lefschetz (1,1) theorem syas-theorem says that the cycle map $$ \text{cl}:Pic(M) \to \text{Hod}^1(M) $$$$ \text{cl}:\operatorname{Pic}(M) \to \text{Hod}^1(M) $$ is surjective.

Quesion. Is there an interesting example of (1,1)-form $\omega \in H^1(M,\Omega_M^1)$ which isn`t spanned by $Pic(M)_{\mathbb{C}}$?

Question. Is there an interesting example of (1,1)-form $\omega \in H^1(M,\Omega_M^1)$ which isn`t spanned by $\operatorname{Pic}(M)_{\mathbb{C}}$?

(1,1)-form doesn`t come from divisor

Let $M$ be projective complex manifold. The Lefschetz (1,1) theorem syas that the cycle map $$ \text{cl}:Pic(M) \to \text{Hod}^1(M) $$ is surjective.

Quesion. Is there an interesting example of (1,1)-form $\omega \in H^1(M,\Omega_M^1)$ which isn`t spanned by $Pic(M)_{\mathbb{C}}$?

(1,1)-form that does not come from a divisor

Let $M$ be projective complex manifold. The Lefschetz (1,1)-theorem says that the cycle map $$ \text{cl}:\operatorname{Pic}(M) \to \text{Hod}^1(M) $$ is surjective.

Question. Is there an interesting example of (1,1)-form $\omega \in H^1(M,\Omega_M^1)$ which isn`t spanned by $\operatorname{Pic}(M)_{\mathbb{C}}$?

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user145752
user145752
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(1,1)-form doesn`t come from divisor

Let $M$ be projective complex manifold. The Lefschetz (1,1) theorem syas that the cycle map $$ \text{cl}:Pic(M) \to \text{Hod}^1(M) $$ is surjective.

Quesion. Is there an interesting example of (1,1)-form $\omega \in H^1(M,\Omega_M^1)$ which isn`t spanned by $Pic(M)_{\mathbb{C}}$?