I am looking for text books/notes/papers/documents playing with toy examples: projective space, in particular, $P^{1}$. Because I think this is really a cute example. Although algebraic geometry on $P^{1}$ is comparatively simple, it gave inspirations to treat more general situtation. Precisely, I am looking for something including following topics:(but you can add whatever you want)

algebraic geometry of $P^{n}$, say, $Coh(P^{n})$, $D^{b}(Coh(P^{n}))$, say, exceptional collection,semi-orthogonal decomposition,stability conditions

Relation to representation theory, say, Hall algebra of $Coh(P^{n})$ and $D^{b}(Coh(P^{n}))$ and its relation to affine quantum group: $U_{q}(\hat{sl_{n+1}})$, representation theory of Kronecker quiver. Tilting theory. Weighted projective line and so on.

$D-module$ on flag variety of $U(sl_{2})$(or $P^{1}$) and so on..................

Add whatever you like.

Add whatever you like.

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