8 Topics in Moduli Theory

• Chapter 108: Moduli Stacks
  • Section 108.1: Introduction
  • Section 108.2: Conventions and abuse of language
  • Section 108.3: Properties of Hom and Isom
  • Section 108.4: Properties of the stack of coherent sheaves
  • Section 108.5: Properties of Quot
  • Section 108.6: Boundedness for Quot
  • Section 108.7: Properties of the Hilbert functor
  • Section 108.8: Properties of the Picard stack
  • Section 108.9: Properties of the Picard functor
  • Section 108.10: Properties of relative morphisms
  • Section 108.11: Properties of the stack of polarized proper schemes
  • Section 108.12: Properties of moduli of complexes on a proper morphism
• Chapter 109: Moduli of Curves
  • Section 109.1: Introduction
  • Section 109.2: Conventions and abuse of language
  • Section 109.3: The stack of curves
  • Section 109.4: The stack of polarized curves
  • Section 109.5: Properties of the stack of curves
  • Section 109.6: Open substacks of the stack of curves
  • Section 109.7: Curves with finite reduced automorphism groups
  • Section 109.8: Cohen-Macaulay curves
  • Section 109.9: Curves of a given genus
  • Section 109.10: Geometrically reduced curves
  • Section 109.11: Geometrically reduced and connected curves
  • Section 109.12: Gorenstein curves
  • Section 109.13: Local complete intersection curves
  • Section 109.14: Curves with isolated singularities
  • Section 109.15: The smooth locus of the stack of curves
  • Section 109.16: Smooth curves
  • Section 109.17: Density of smooth curves
  • Section 109.18: Nodal curves
  • Section 109.19: The relative dualizing sheaf
  • Section 109.20: Prestable curves
  • Section 109.21: Semistable curves
  • Section 109.22: Stable curves
  • Section 109.23: Contraction morphisms
  • Section 109.24: Stable reduction theorem
  • Section 109.25: Properties of the stack of stable curves