8 Topics in Moduli Theory

• Chapter 106: Moduli Stacks
  • Section 106.1: Introduction
  • Section 106.2: Conventions and abuse of language
  • Section 106.3: Properties of Hom and Isom
  • Section 106.4: Properties of the stack of coherent sheaves
  • Section 106.5: Properties of Quot
  • Section 106.6: Boundedness for Quot
  • Section 106.7: Properties of the Hilbert functor
  • Section 106.8: Properties of the Picard stack
  • Section 106.9: Properties of the Picard functor
  • Section 106.10: Properties of relative morphisms
  • Section 106.11: Properties of the stack of polarized proper schemes
  • Section 106.12: Properties of moduli of complexes on a proper morphism
• Chapter 107: Moduli of Curves
  • Section 107.1: Introduction
  • Section 107.2: Conventions and abuse of language
  • Section 107.3: The stack of curves
  • Section 107.4: The stack of polarized curves
  • Section 107.5: Properties of the stack of curves
  • Section 107.6: Open substacks of the stack of curves
  • Section 107.7: Curves with finite reduced automorphism groups
  • Section 107.8: Cohen-Macaulay curves
  • Section 107.9: Curves of a given genus
  • Section 107.10: Geometrically reduced curves
  • Section 107.11: Geometrically reduced and connected curves
  • Section 107.12: Gorenstein curves
  • Section 107.13: Local complete intersection curves
  • Section 107.14: Curves with isolated singularities
  • Section 107.15: The smooth locus of the stack of curves
  • Section 107.16: Smooth curves
  • Section 107.17: Density of smooth curves
  • Section 107.18: Nodal curves
  • Section 107.19: The relative dualizing sheaf
  • Section 107.20: Prestable curves
  • Section 107.21: Semistable curves
  • Section 107.22: Stable curves
  • Section 107.23: Contraction morphisms
  • Section 107.24: Stable reduction theorem
  • Section 107.25: Properties of the stack of stable curves