All Questions

In this post, an answer claims that the normal bundle of the Veronese decomposes into a filtration, such that the associated graded is $$\bigoplus_{i=2}^d S^i T,$$ where $T$ is the tangent bundle. But ...

Given a cotangent bundle of a projective variety $Y=T^*X,$ do we know that its affinization map, $$Y \rightarrow \mathrm{Spec}(H^0(Y,\mathscr{O}_Y))$$ is proper or projective?

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-...