8 Topics in Moduli Theory

• Chapter 107: Moduli Stacks
  • Section 107.1: Introduction
  • Section 107.2: Conventions and abuse of language
  • Section 107.3: Properties of Hom and Isom
  • Section 107.4: Properties of the stack of coherent sheaves
  • Section 107.5: Properties of Quot
  • Section 107.6: Boundedness for Quot
  • Section 107.7: Properties of the Hilbert functor
  • Section 107.8: Properties of the Picard stack
  • Section 107.9: Properties of the Picard functor
  • Section 107.10: Properties of relative morphisms
  • Section 107.11: Properties of the stack of polarized proper schemes
  • Section 107.12: Properties of moduli of complexes on a proper morphism
• Chapter 108: Moduli of Curves
  • Section 108.1: Introduction
  • Section 108.2: Conventions and abuse of language
  • Section 108.3: The stack of curves
  • Section 108.4: The stack of polarized curves
  • Section 108.5: Properties of the stack of curves
  • Section 108.6: Open substacks of the stack of curves
  • Section 108.7: Curves with finite reduced automorphism groups
  • Section 108.8: Cohen-Macaulay curves
  • Section 108.9: Curves of a given genus
  • Section 108.10: Geometrically reduced curves
  • Section 108.11: Geometrically reduced and connected curves
  • Section 108.12: Gorenstein curves
  • Section 108.13: Local complete intersection curves
  • Section 108.14: Curves with isolated singularities
  • Section 108.15: The smooth locus of the stack of curves
  • Section 108.16: Smooth curves
  • Section 108.17: Density of smooth curves
  • Section 108.18: Nodal curves
  • Section 108.19: The relative dualizing sheaf
  • Section 108.20: Prestable curves
  • Section 108.21: Semistable curves
  • Section 108.22: Stable curves
  • Section 108.23: Contraction morphisms
  • Section 108.24: Stable reduction theorem
  • Section 108.25: Properties of the stack of stable curves