Singular curves and quasi-hereditary algebras
| Autor: | Igor Burban, Yuriy Drozd, Volodymyr Gavran |
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| Rok vydání: | 2015 |
| Předmět: |
Subcategory
Normalization (statistics) 14F05 14A22 16E35 Pure mathematics Derived category Triangulated category General Mathematics 010102 general mathematics Resolution of singularities 01 natural sciences Coherent sheaf Mathematics - Algebraic Geometry Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Sheaf 010307 mathematical physics 0101 mathematics Representation Theory (math.RT) Mathematics::Representation Theory Categorical variable Algebraic Geometry (math.AG) Mathematics - Representation Theory Mathematics |
| Zdroj: | International Mathematics Research Notices |
| DOI: | 10.48550/arxiv.1503.04565 |
| Popis: | 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 $\Lambda$ such that the triangulated category of perfect complexes on $X$ embeds into $D^b(\Lambda-\mathsf{mod})$ as a full subcategory. Comment: minor changes; to appear in IMRN |
| Databáze: | OpenAIRE |
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