On embedded products of Grassmannians

Abstract

Let ${\Gamma }^{\prime }$ and $\Gamma$ be two Grassmannians. The standard embedding $\varphi :{\Gamma }^{\prime }\times \Gamma \to \bar{P}$ is obtained by combining the Plücker and Segre embeddings. Given a further embedding $\eta :{\Gamma }^{\prime }\times \Gamma \to P^{\prime }$, we find a sufficient condition for the existence of $\alpha \in Aut(\Gamma )$ and of a collineation $\psi :\bar{P}\to P^{\prime }$ such that $\eta =({\mathrm{id}}_{{\Gamma }^{\prime }}\times \alpha )\varphi \psi$.

References in corpus (3)

• The Veronese Surface in PG(5,3) and Witt's 5-$(12,6,1$ Design
• Giuseppe Veronese and Ernst Witt -- Neighbours in PG(5,3)
• A Dimension Formula for the Nucleus of a Veronese Variety

Cited by in corpus (3)

• Nets of conics of rank one in PG(2,q), q odd
• Lifting of divisible designs
• The symmetric representation of lines in $\text{PG}({\mathbb{F}}^3\otimes {\mathbb{F}}^3)$