Moduli spaces and stacks

Aim: introduce moduli spaces of Bridgeland semistable objects. References: see this survey by Gomez for a quick introduction to stalks and these notes by Alper for more details.

• Motivation: a short discussion about moduli problems, (co)representability of the moduli functor, moduli stacks.
• Algebraic spaces and stalks: introduce the étale site, define algebraic spaces and Artin stalks (Section 2.1 of Alper's notes).
• Bridgeland moduli spaces: introduce the moduli stack of perfect complexes and its substack of Bridgeland semistable objects, state Theorem 5.20, discuss Question 5.23 (mention the existence of good moduli spaces as defined by Alper) and 5.24 from Macrì-Schmidt's notes.
• Moduli over K3 surfaces: briefly recall stability conditions for K3 surfaces and state Theorem 6.34 of Macrì-Schmidt's notes.
Video of the talk