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Fine Compactified Moduli of Enriched Structures on Stable Curves
About this Title
Owen Biesel and David Holmes
Publication: Memoirs of the American Mathematical Society
Publication Year:
2023; Volume 285, Number 1416
ISBNs: 978-1-4704-6310-6 (print); 978-1-4704-7486-7 (online)
DOI: https://doi.org/10.1090/memo/1416
Published electronically: April 25, 2023
Table of Contents
Chapters
- 1. Introduction
1. Fine moduli of enriched structures
- 2. Preliminaries
- 3. Defining enriched structures
- 4. Representability of the functor of enriched structures
- 5. Enriched structures over separably closed fields
- 6. The stack of enriched structures and universal Néron models
- 7. Relation to the constructions of Mainò
2. Compactifying the stack of enriched structures
- 8. Defining compactified enriched structures
- 9. Properness of the stack of compactified enriched structures
- 10. Comparison to enriched structures
- A. Defining sheaves on a base for a Grothendieck topology
- Index of notation
Abstract
Enriched structures on stable curves over fields were defined by Mainò in the late 1990s, and have played an important role in the study of limit linear series and degenerating jacobians. In this paper we solve three main problems: we give a definition of enriched structures on stable curves over arbitrary base schemes, and show that the resulting fine moduli problem is representable; we show that the resulting object has a universal property in terms of Néron models; and we construct a compactification of our stack of enriched structures.- Allen B. Altman and Steven L. Kleiman, Compactifying the Picard scheme, Adv. in Math. 35 (1980), no. 1, 50–112. MR 555258, DOI 10.1016/0001-8708(80)90043-2
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