101 Moduli of Curves

Section 101.1: Introduction
Section 101.2: Conventions and abuse of language
Section 101.3: The stack of curves
- Lemma 101.3.1
Section 101.4: The stack of polarized curves
- Lemma 101.4.1
- Lemma 101.4.2
- Lemma 101.4.3
Section 101.5: Properties of the stack of curves
- Lemma 101.5.1
- Remark 101.5.2
- Lemma 101.5.3
Section 101.6: Open substacks of the stack of curves
Section 101.7: Curves with finite reduced automorphism groups
- Example 101.7.1: Non-reduced automorphism group
- Example 101.7.2: Smooth positive dimensional automorphism group
- Lemma 101.7.3
- Lemma 101.7.4
Section 101.8: Cohen-Macaulay curves
- Lemma 101.8.1
- Lemma 101.8.2
Section 101.9: Curves of a given genus
- Lemma 101.9.1
- Lemma 101.9.2
- Lemma 101.9.3
- Lemma 101.9.4
Section 101.10: Geometrically reduced curves
- Lemma 101.10.1
- Lemma 101.10.2
Section 101.11: Geometrically reduced and connected curves
- Lemma 101.11.1
- Lemma 101.11.2
- Lemma 101.11.3
Section 101.12: Gorenstein curves
- Lemma 101.12.1
- Lemma 101.12.2
Section 101.13: Local complete intersection curves
- Lemma 101.13.1
Section 101.14: Curves with isolated singularities
- Lemma 101.14.1
Section 101.15: The smooth locus of the stack of curves
- Lemma 101.15.1
- Lemma 101.15.2
Section 101.16: Smooth curves
- Lemma 101.16.1
- Lemma 101.16.2
- Lemma 101.16.3
- Definition 101.16.4 reference
- Lemma 101.16.5
- Lemma 101.16.6
Section 101.17: Density of smooth curves
- Lemma 101.17.1
Section 101.18: Nodal curves
- Lemma 101.18.1
- Lemma 101.18.2
Section 101.19: The relative dualizing sheaf
- Lemma 101.19.1
- Definition 101.19.2
- Lemma 101.19.3
Section 101.20: Prestable curves
- Definition 101.20.1
- Lemma 101.20.2
- Lemma 101.20.3
- Lemma 101.20.4
Section 101.21: Semistable curves
- Lemma 101.21.1
- Definition 101.21.2
- Lemma 101.21.3
- Lemma 101.21.4
- Lemma 101.21.5
Section 101.22: Stable curves
- Lemma 101.22.1
- Definition 101.22.2
- Lemma 101.22.3
- Definition 101.22.4 reference
- Lemma 101.22.5
- Lemma 101.22.6
- Lemma 101.22.7
- Lemma 101.22.8
Section 101.23: Contraction morphisms
- Lemma 101.23.1
- Lemma 101.23.2
- Lemma 101.23.3
- Lemma 101.23.4
- Lemma 101.23.5
Section 101.24: Stable reduction theorem
- Lemma 101.24.1
- Lemma 101.24.2
- Theorem 101.24.3 reference
Section 101.25: Properties of the stack of stable curves
- Lemma 101.25.1
- Lemma 101.25.2
- Theorem 101.25.3