106 Moduli of Curves

Section 106.1: Introduction
Section 106.2: Conventions and abuse of language
Section 106.3: The stack of curves
- Lemma 106.3.1
Section 106.4: The stack of polarized curves
- Lemma 106.4.1
- Lemma 106.4.2
- Lemma 106.4.3
Section 106.5: Properties of the stack of curves
- Lemma 106.5.1
- Remark 106.5.2
- Lemma 106.5.3
Section 106.6: Open substacks of the stack of curves
Section 106.7: Curves with finite reduced automorphism groups
- Example 106.7.1: Non-reduced automorphism group
- Example 106.7.2: Smooth positive dimensional automorphism group
- Lemma 106.7.3
- Lemma 106.7.4
Section 106.8: Cohen-Macaulay curves
- Lemma 106.8.1
- Lemma 106.8.2
Section 106.9: Curves of a given genus
- Lemma 106.9.1
- Lemma 106.9.2
- Lemma 106.9.3
- Lemma 106.9.4
Section 106.10: Geometrically reduced curves
- Lemma 106.10.1
- Lemma 106.10.2
Section 106.11: Geometrically reduced and connected curves
- Lemma 106.11.1
- Lemma 106.11.2
- Lemma 106.11.3
Section 106.12: Gorenstein curves
- Lemma 106.12.1
- Lemma 106.12.2
Section 106.13: Local complete intersection curves
- Lemma 106.13.1
Section 106.14: Curves with isolated singularities
- Lemma 106.14.1
Section 106.15: The smooth locus of the stack of curves
- Lemma 106.15.1
- Lemma 106.15.2
Section 106.16: Smooth curves
- Lemma 106.16.1
- Lemma 106.16.2
- Lemma 106.16.3
- Definition 106.16.4 reference
- Lemma 106.16.5
- Lemma 106.16.6
Section 106.17: Density of smooth curves
- Lemma 106.17.1
Section 106.18: Nodal curves
- Lemma 106.18.1
- Lemma 106.18.2
Section 106.19: The relative dualizing sheaf
- Lemma 106.19.1
- Definition 106.19.2
- Lemma 106.19.3
Section 106.20: Prestable curves
- Definition 106.20.1
- Lemma 106.20.2
- Lemma 106.20.3
- Lemma 106.20.4
Section 106.21: Semistable curves
- Lemma 106.21.1
- Definition 106.21.2
- Lemma 106.21.3
- Lemma 106.21.4
- Lemma 106.21.5
Section 106.22: Stable curves
- Lemma 106.22.1
- Definition 106.22.2
- Lemma 106.22.3
- Definition 106.22.4 reference
- Lemma 106.22.5
- Lemma 106.22.6
- Lemma 106.22.7
- Lemma 106.22.8
Section 106.23: Contraction morphisms
- Lemma 106.23.1
- Lemma 106.23.2
- Lemma 106.23.3
- Lemma 106.23.4
- Lemma 106.23.5
Section 106.24: Stable reduction theorem
- Lemma 106.24.1
- Lemma 106.24.2
- Theorem 106.24.3 reference
Section 106.25: Properties of the stack of stable curves
- Lemma 106.25.1
- Lemma 106.25.2
- Theorem 106.25.3