108 Moduli of Curves

Section 108.1: Introduction
Section 108.2: Conventions and abuse of language
Section 108.3: The stack of curves
- Lemma 108.3.1
Section 108.4: The stack of polarized curves
- Lemma 108.4.1
- Lemma 108.4.2
- Lemma 108.4.3
Section 108.5: Properties of the stack of curves
- Lemma 108.5.1
- Remark 108.5.2
- Lemma 108.5.3
Section 108.6: Open substacks of the stack of curves
Section 108.7: Curves with finite reduced automorphism groups
- Example 108.7.1: Non-reduced automorphism group
- Example 108.7.2: Smooth positive dimensional automorphism group
- Lemma 108.7.3
- Lemma 108.7.4
Section 108.8: Cohen-Macaulay curves
- Lemma 108.8.1
- Lemma 108.8.2
Section 108.9: Curves of a given genus
- Lemma 108.9.1
- Lemma 108.9.2
- Lemma 108.9.3
- Lemma 108.9.4
Section 108.10: Geometrically reduced curves
- Lemma 108.10.1
- Lemma 108.10.2
Section 108.11: Geometrically reduced and connected curves
- Lemma 108.11.1
- Lemma 108.11.2
- Lemma 108.11.3
Section 108.12: Gorenstein curves
- Lemma 108.12.1
- Lemma 108.12.2
Section 108.13: Local complete intersection curves
- Lemma 108.13.1
Section 108.14: Curves with isolated singularities
- Lemma 108.14.1
Section 108.15: The smooth locus of the stack of curves
- Lemma 108.15.1
- Lemma 108.15.2
Section 108.16: Smooth curves
- Lemma 108.16.1
- Lemma 108.16.2
- Lemma 108.16.3
- Definition 108.16.4 reference
- Lemma 108.16.5
- Lemma 108.16.6
Section 108.17: Density of smooth curves
- Lemma 108.17.1
Section 108.18: Nodal curves
- Lemma 108.18.1
- Lemma 108.18.2
Section 108.19: The relative dualizing sheaf
- Lemma 108.19.1
- Definition 108.19.2
- Lemma 108.19.3
Section 108.20: Prestable curves
- Definition 108.20.1
- Lemma 108.20.2
- Lemma 108.20.3
- Lemma 108.20.4
Section 108.21: Semistable curves
- Lemma 108.21.1
- Definition 108.21.2
- Lemma 108.21.3
- Lemma 108.21.4
- Lemma 108.21.5
Section 108.22: Stable curves
- Lemma 108.22.1
- Definition 108.22.2
- Lemma 108.22.3
- Definition 108.22.4 reference
- Lemma 108.22.5
- Lemma 108.22.6
- Lemma 108.22.7
- Lemma 108.22.8
Section 108.23: Contraction morphisms
- Lemma 108.23.1
- Lemma 108.23.2
- Lemma 108.23.3
- Lemma 108.23.4
- Lemma 108.23.5
Section 108.24: Stable reduction theorem
- Lemma 108.24.1
- Lemma 108.24.2
- Theorem 108.24.3 reference
Section 108.25: Properties of the stack of stable curves
- Lemma 108.25.1
- Lemma 108.25.2
- Theorem 108.25.3