Resolution of the Diagonal on the Root Stacks

TL;DR

This paper provides a new constructive proof for the semi-orthogonal decomposition of the derived category of root stacks by explicitly resolving the diagonal, enhancing understanding of their categorical structure.

Contribution

It introduces an explicit resolution of the diagonal to prove semi-orthogonal decompositions in root stacks, offering a constructive approach.

Findings

Explicit resolution of the diagonal for root stacks

New constructive proof of semi-orthogonal decomposition

Enhanced understanding of derived categories of root stacks

Abstract

In this paper, we give a new constructive proof of the semi-orthogonal decomposition of the derived category of (quasi)-coherent sheaves of root stacks, through an explicit resolution of the diagonal.