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: CohenMacaulay 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