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: CohenMacaulay 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