TL;DR
This paper introduces a categorical refinement of the blowup process in algebraic geometry by utilizing filtered derived categories to unify two steps of categorical resolution of singularities.
Contribution
It presents a novel approach that combines the steps of categorical resolution into a single, natural refinement of the blowup process using filtered derived categories.
Findings
Unified the two-step categorical resolution into one process
Provided a natural categorical refinement of the blowup
Enhanced understanding of resolutions of singularities
Abstract
Categorical resolution of singularities has been constructed in arXiv:1212.6170. It proceeds by alternating two steps of seemingly different nature. We show how to use the formalism of filtered derived categories to combine the two steps into one. This results in a certain rather natural categorical refinement of the usual blowup of an algebraic variety in a closed subscheme.
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