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Projectivization of the normal bundle of $\mathbb P^4$ in the 10-spinor variety
Let $X=S_{10} \subset \mathbb P^{15}$ be the 10-dimensional spinor variety in its minimal embedding. Consider a $\mathbb P^4 \subset S_{10}$, hence we can define the normal bundle $N=N_{\mathbb P^4|S_{...
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Tangent bundle for orthogonal and isotropic Grassmannians
We will work over $\mathbb C$. Let us consider a $n$-dimensional vector space $V$, then we define the $k$-th Grassmannian as
$$
\mathbb G(k,V):=\{W \subset V : \dim W=k\}.
$$
Then consider a non-...