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: CohenMacaulay 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