The inverse Serre functor of D^b_c(P^n) is the P-twist at the IC sheaf of the open stratum, and all indecomposable perverse sheaves are P-like or 0-spherical.
Formality of P-objects
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Serre functor and $\mathbb{P}$-objects for perverse sheaves on $\mathbb{P}^n$
The inverse Serre functor of D^b_c(P^n) is the P-twist at the IC sheaf of the open stratum, and all indecomposable perverse sheaves are P-like or 0-spherical.