107 Moduli of Curves

Section 107.1: Introduction
Section 107.2: Conventions and abuse of language
Section 107.3: The stack of curves
- Lemma 107.3.1
Section 107.4: The stack of polarized curves
- Lemma 107.4.1
- Lemma 107.4.2
- Lemma 107.4.3
Section 107.5: Properties of the stack of curves
- Lemma 107.5.1
- Remark 107.5.2
- Lemma 107.5.3
Section 107.6: Open substacks of the stack of curves
Section 107.7: Curves with finite reduced automorphism groups
- Example 107.7.1: Non-reduced automorphism group
- Example 107.7.2: Smooth positive dimensional automorphism group
- Lemma 107.7.3
- Lemma 107.7.4
Section 107.8: Cohen-Macaulay curves
- Lemma 107.8.1
- Lemma 107.8.2
Section 107.9: Curves of a given genus
- Lemma 107.9.1
- Lemma 107.9.2
- Lemma 107.9.3
- Lemma 107.9.4
Section 107.10: Geometrically reduced curves
- Lemma 107.10.1
- Lemma 107.10.2
Section 107.11: Geometrically reduced and connected curves
- Lemma 107.11.1
- Lemma 107.11.2
- Lemma 107.11.3
Section 107.12: Gorenstein curves
- Lemma 107.12.1
- Lemma 107.12.2
Section 107.13: Local complete intersection curves
- Lemma 107.13.1
Section 107.14: Curves with isolated singularities
- Lemma 107.14.1
Section 107.15: The smooth locus of the stack of curves
- Lemma 107.15.1
- Lemma 107.15.2
Section 107.16: Smooth curves
- Lemma 107.16.1
- Lemma 107.16.2
- Lemma 107.16.3
- Definition 107.16.4 reference
- Lemma 107.16.5
- Lemma 107.16.6
Section 107.17: Density of smooth curves
- Lemma 107.17.1
Section 107.18: Nodal curves
- Lemma 107.18.1
- Lemma 107.18.2
Section 107.19: The relative dualizing sheaf
- Lemma 107.19.1
- Definition 107.19.2
- Lemma 107.19.3
Section 107.20: Prestable curves
- Definition 107.20.1
- Lemma 107.20.2
- Lemma 107.20.3
- Lemma 107.20.4
Section 107.21: Semistable curves
- Lemma 107.21.1
- Definition 107.21.2
- Lemma 107.21.3
- Lemma 107.21.4
- Lemma 107.21.5
Section 107.22: Stable curves
- Lemma 107.22.1
- Definition 107.22.2
- Lemma 107.22.3
- Definition 107.22.4 reference
- Lemma 107.22.5
- Lemma 107.22.6
- Lemma 107.22.7
- Lemma 107.22.8
Section 107.23: Contraction morphisms
- Lemma 107.23.1
- Lemma 107.23.2
- Lemma 107.23.3
- Lemma 107.23.4
- Lemma 107.23.5
Section 107.24: Stable reduction theorem
- Lemma 107.24.1
- Lemma 107.24.2
- Theorem 107.24.3 reference
Section 107.25: Properties of the stack of stable curves
- Lemma 107.25.1
- Lemma 107.25.2
- Theorem 107.25.3