Tangent bundle of a manifold of K$3^{[2]}$-type is rigid
We prove that the tangent bundle of a manifold of K$3^{[2]}$-type is rigid.
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arXiv subjects
Volodymyr Gavran
Publications and source records attributed to Volodymyr Gavran.
Minors and resolutions of non-commutative schemes
In this article we develop the theory of minors of non-commutative schemes. This study is motivated by applications in the theory of non-commutative resolutions of singularities of commutative schemes. In particular, we construct a categorical resolution for non-commutative curves and in the rational case show that it can be realized as the derived category of a quasi-hereditary algebra.
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Singular curves and quasi-hereditary algebras
In this article we construct a categorical resolution of singularities of an excellent reduced curve $X$, introducing a certain sheaf of orders on $X$. This categorical resolution is shown to be a recollement of the derived category of coherent sheaves on the normalization of $X$ and the derived category of finite length modules over a certain artinian quasi-hereditary ring $Q$ depending purely on the local singularity types of $X$. Using this technique, we prove several statements on the Rouquier dimension of the derived category of coherent sheaves on $X$. Moreover, in the case $X$ is rational and projective we construct a finite dimensional quasi-hereditary algebra $Λ$ such that the triangulated category of perfect complexes on $X$ embeds into $D^b(Λ-\mathsf{mod})$ as a full subcategory.
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