8 Topics in Moduli Theory

Chapter 105: Moduli Stacks
- Section 105.1: Introduction
- Section 105.2: Conventions and abuse of language
- Section 105.3: Properties of Hom and Isom
- Section 105.4: Properties of the stack of coherent sheaves
- Section 105.5: Properties of Quot
- Section 105.6: Boundedness for Quot
- Section 105.7: Properties of the Hilbert functor
- Section 105.8: Properties of the Picard stack
- Section 105.9: Properties of the Picard functor
- Section 105.10: Properties of relative morphisms
- Section 105.11: Properties of the stack of polarized proper schemes
- Section 105.12: Properties of moduli of complexes on a proper morphism
Chapter 106: Moduli of Curves
- Section 106.1: Introduction
- Section 106.2: Conventions and abuse of language
- Section 106.3: The stack of curves
- Section 106.4: The stack of polarized curves
- Section 106.5: Properties of the stack of curves
- Section 106.6: Open substacks of the stack of curves
- Section 106.7: Curves with finite reduced automorphism groups
- Section 106.8: Cohen-Macaulay curves
- Section 106.9: Curves of a given genus
- Section 106.10: Geometrically reduced curves
- Section 106.11: Geometrically reduced and connected curves
- Section 106.12: Gorenstein curves
- Section 106.13: Local complete intersection curves
- Section 106.14: Curves with isolated singularities
- Section 106.15: The smooth locus of the stack of curves
- Section 106.16: Smooth curves
- Section 106.17: Density of smooth curves
- Section 106.18: Nodal curves
- Section 106.19: The relative dualizing sheaf
- Section 106.20: Prestable curves
- Section 106.21: Semistable curves
- Section 106.22: Stable curves
- Section 106.23: Contraction morphisms
- Section 106.24: Stable reduction theorem
- Section 106.25: Properties of the stack of stable curves