arXiv subjects
Publications and source records attributed to Lukas Bonfert.
We show that the inverse Serre functor for the constructible derived category $\mathbf{D}^\mathrm{b}_\mathrm{c}(\mathbb{P}^n)$ is given by the $\mathbb{P}$-twist at the simple perverse sheaf corresponding to the open stratum. Moreover, we show that all indecomposable perverse sheaves on $\mathbb{P}^n$ are $\mathbb{P}$-like objects, and explicitly construct morphisms spanning their total endomorphism spaces.
We provide a convenient formulation of the definition of Cartan graphs and Weyl groupoids introduced by Heckenberger and Schneider, and construct Cartan graphs for regular symmetrizable contragredient Lie superalgebras. For $\mathfrak{sl}(m|n)$, $\mathfrak{osp}(2m+1|2n)$ and $\mathfrak{osp}(2m|2n)$ we explicitly describe the Cartan graph in terms of partitions and determine the relations between the generators of their Weyl groupoids.
We introduce derived projective covers and explain how they are related to the notion of enough derived projectives. This provides an if-and-only-if criterion for when derived projective covers form a silting collection. We prove moreover a Koszul duality result for silting and simple-minded collections.