On Mukai flops for Scorza varieties

Abstract

I give three descriptions of the Mukai flop of type $E\_{6,I}$, one in terms of Jordan algebras, one in terms of projective geometry over the octonions, and one in terms of O-blow-ups. Each description shows that it is very similar to certain flops of type $A$. The Mukai flop of type $E\_{6,II}$ is also described.