On embedded products of Grassmannians

The standard embedding \phi the product of two Grassmannians is obtained by combining the Pl\ufccker and Segre embeddings. Given a further embedding \eta, we find a sufficient condition for the existence of an automorphism \alpha of the first Grassmannian and of a collineation \psi such that \eta=(id\Gamma'\times\alpha)\phi\psi

On embedded products of Grassmannians

Let and be two Grassmannians. The standard embedding : ! P is obtained by combining the Plücker and Segre embeddings. Given