The Stacks project

\begin{equation*} \DeclareMathOperator\Coim{Coim} \DeclareMathOperator\Coker{Coker} \DeclareMathOperator\Ext{Ext} \DeclareMathOperator\Hom{Hom} \DeclareMathOperator\Im{Im} \DeclareMathOperator\Ker{Ker} \DeclareMathOperator\Mor{Mor} \DeclareMathOperator\Ob{Ob} \DeclareMathOperator\Sh{Sh} \DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}} \DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}} \DeclareMathOperator\Spec{Spec} \newcommand\colim{\mathop{\mathrm{colim}}\nolimits} \newcommand\lim{\mathop{\mathrm{lim}}\nolimits} \newcommand\Qcoh{\mathit{Qcoh}} \newcommand\Sch{\mathit{Sch}} \newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}} \newcommand\Cohstack{\mathcal{C}\!\mathit{oh}} \newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}} \newcommand\Quotfunctor{\mathrm{Quot}} \newcommand\Hilbfunctor{\mathrm{Hilb}} \newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}} \newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}} \newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}} \newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits} \newcommand\Picardstack{\mathcal{P}\!\mathit{ic}} \newcommand\Picardfunctor{\mathrm{Pic}} \newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}} \end{equation*}

8 Topics in Moduli Theory

  • Chapter 100: Moduli Stacks
    • Section 100.1: Introduction
    • Section 100.2: Conventions and abuse of language
    • Section 100.3: Properties of Hom and Isom
    • Section 100.4: Properties of the stack of coherent sheaves
    • Section 100.5: Properties of Quot
    • Section 100.6: Boundedness for Quot
    • Section 100.7: Properties of the Hilbert functor
    • Section 100.8: Properties of the Picard stack
    • Section 100.9: Properties of the Picard functor
    • Section 100.10: Properties of relative morphisms
    • Section 100.11: Properties of the stack of polarized proper schemes
    • Section 100.12: Properties of moduli of complexes on a proper morphism
  • Chapter 101: Moduli of Curves
    • Section 101.1: Introduction
    • Section 101.2: Conventions and abuse of language
    • Section 101.3: The stack of curves
    • Section 101.4: The stack of polarized curves
    • Section 101.5: Properties of the stack of curves
    • Section 101.6: Open substacks of the stack of curves
    • Section 101.7: Curves with finite reduced automorphism groups
    • Section 101.8: Cohen-Macaulay curves
    • Section 101.9: Curves of a given genus
    • Section 101.10: Geometrically reduced curves
    • Section 101.11: Geometrically reduced and connected curves
    • Section 101.12: Gorenstein curves
    • Section 101.13: Local complete intersection curves
    • Section 101.14: Curves with isolated singularities
    • Section 101.15: The smooth locus of the stack of curves
    • Section 101.16: Smooth curves
    • Section 101.17: Density of smooth curves
    • Section 101.18: Nodal curves
    • Section 101.19: The relative dualizing sheaf
    • Section 101.20: Prestable curves
    • Section 101.21: Semistable curves
    • Section 101.22: Stable curves
    • Section 101.23: Contraction morphisms
    • Section 101.24: Stable reduction theorem
    • Section 101.25: Properties of the stack of stable curves