Abelian 3-folds in products of projective spaces (Q1893427)

In the present paper the author shows that there exist no abelian 3-folds in the product of projective spaces \(\mathbb{P}^1\times \mathbb{P}^4\) and \(\mathbb{P}^2\times \mathbb{P}^3\). By assuming that an abelian 3-fold \(X\) is in such a product of projective spaces, the author calculates the self-intersection class \([X]^2\) and obtains a contradition.