Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 Projectivity of the moduli of curves
- 2 The stack of admissible covers is algebraic
- 3 Projectivity of the moduli space of vector bundles on a curve
- 4 Boundedness of semistable sheaves
- 5 Theorem of the Base
- 6 Weil restriction for schemes and beyond
- 7 Heights over finitely generated fields
- 8 An explicit self-duality
- 9 Tannakian reconstruction of coalgebroids
1 - Projectivity of the moduli of curves
Published online by Cambridge University Press: 06 October 2022
Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 Projectivity of the moduli of curves
- 2 The stack of admissible covers is algebraic
- 3 Projectivity of the moduli space of vector bundles on a curve
- 4 Boundedness of semistable sheaves
- 5 Theorem of the Base
- 6 Weil restriction for schemes and beyond
- 7 Heights over finitely generated fields
- 8 An explicit self-duality
- 9 Tannakian reconstruction of coalgebroids
Summary
In this expository paper, we show that the Deligne–Mumford moduli space of stable curves is projective over Spec (Ζ). The proof we exposit is due to Kollár. Ampleness of a line bundle is deduced from nefness of a related vector bundle via the Ampleness Lemma, a classifying map construction. The main positivity result concerns the pushforward of relative dualizing sheaves on families of stable curves over a smooth projective curve.
- Type
- Chapter
- Information
- Stacks Project Expository Collection , pp. 1 - 43Publisher: Cambridge University PressPrint publication year: 2022