S-equivalence for algebraic stacks

TL;DR

This paper extends the concept of S-equivalence from semistable vector bundles to points in algebraic stacks, aiding in understanding moduli space identifications and their properties.

Contribution

It introduces a generalized S-equivalence for algebraic stacks and explores its implications for moduli space structure and separatedness.

Findings

Recovered classical S-equivalence for vector bundles

Described point identification in moduli spaces

Discussed relation to separatedness of moduli spaces

Abstract

We generalize the notion of S-equivalence, previously defined for semistable vector bundles, to points in arbitrary algebraic stacks and use it to describe the identification of points when passing to the moduli space. As applications, we recover the classical S-equivalence by considering the identification of semistable vector bundles in the moduli space, and discuss its relation to separatedness of the moduli space.