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The Hermitian symmetric space $M=\mathrm{EIII}$ appears in the classificationof complete simply connected Riemannian manifolds carrying a parallel evenClifford structure. This means the existence of a real oriented Euclideanvector bundle $E$ over it together with an algebra bundle morphism$\varphi:\mathrm{Cl}^0(E) \rightarrow \mathrm{End}(TM)$ mapping $\Lambda^2 E$into skew-symmetric endomorphisms, and the existence of a metric connection on$E$ compatible with $\varphi$. We give an explicit description of such a vectorbundle $E$ as a sub-bundle of $\mathrm{End}(TM)$. From this we construct acanonical differential 8-form on $\mathrm{EIII}$, associated with its holonomy$\mathrm{Spin}(10) \cdot \mathrm{U}(1) \subset \mathrm{U}(16)$, that representsa generator of its cohomology ring. We relate it with a Schubert cyclestructure by looking at $\mathrm{EIII}$ as the smooth projective variety$V_{(4)} \subset \mathbb{C}P^{26}$ known as the fourth Severi variety.

The even Clifford structure of the fourth Severi variety