Proper moduli spaces of orthosymplectic complexes

TL;DR

This paper constructs proper moduli spaces for Bridgeland semistable orthosymplectic complexes, aiming to compactify moduli spaces of principal orthogonal and symplectic bundles, and explores related fixed point and mapping stacks.

Contribution

It introduces a new construction of proper moduli spaces for orthosymplectic complexes, providing a candidate for compactifying principal bundle moduli spaces.

Findings

Constructed proper good moduli spaces for orthosymplectic complexes.

Proved results on good moduli spaces of fixed point stacks.

Analyzed mapping stacks from finite groupoids.

Abstract

We construct proper good moduli spaces for moduli stacks of Bridgeland semistable orthosymplectic complexes on a complex smooth projective variety, which we propose as a candidate for compactifying moduli spaces of principal bundles for the orthogonal and symplectic groups. We also prove some results on good moduli spaces of fixed point stacks and mapping stacks from finite groupoids.