---
- CiteKey: "AT17"
- Type: report
- Title: "ADE surfaces and their moduli," 
- Author: "Alexeev, Valery; Thompson, Alan;"  
- Publisher: "arXiv,"
- Year: 2019 
- Collections: "Affine Dynkin Project,"
---

# ADE surfaces and their moduli

## Meta

- **URL**: <http://arxiv.org/abs/1712.07932>
- **URI**: <http://zotero.org/users/1049732/items/AC4JYFLJ>
- **Local File**: [arXiv Fulltext PDF](file:///home/zack/Zotero/storage/WAR8QI3Q/Alexeev%20and%20Thompson%20-%202019%20-%20ADE%20surfaces%20and%20their%20moduli.pdf); [arXiv.org Snapshot](file:///home/zack/Zotero/storage/MDS2NR9Q/1712.html)
- **Open in Zotero**: [Zotero](zotero://select/library/items/AC4JYFLJ)

## Abstract

We define a class of surfaces corresponding to the ADE root lattices and construct compactifications of their moduli spaces as quotients of projective varieties for Coxeter fans, generalizing Losev-Manin spaces of curves. We exhibit modular families over these moduli spaces, which extend to families of stable pairs over the compactifications. One simple application is a geometric compactification of the moduli of rational elliptic surfaces that is a finite quotient of a projective toric variety.

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## Extracted Annotations


Annotations(5/30/2022, 8:29:04 PM)

-  Defining the moduli space of (weighted) stable curves

![[AT17_HS9VRP3I.png]] [(Alexeev and Thompson, 2019, p. 2)](zotero://open-pdf/library/items/WAR8QI3Q?page=2&annotation=MZ3H53JW)

-  Context (some motivating results)

![[AT17_WSSMNSQN.png]] [(Alexeev and Thompson, 2019, p. 2)](zotero://open-pdf/library/items/WAR8QI3Q?page=2&annotation=TPJTDANE)

-  Main result of this paper.

![[AT17_EYEZ8H4F.png]] [(Alexeev and Thompson, 2019, p. 2)](zotero://open-pdf/library/items/WAR8QI3Q?page=2&annotation=HWQ8GVP4)

-  Definition of surface pairs.

![[AT17_TVNDPLQE.png]] [(Alexeev and Thompson, 2019, p. 2)](zotero://open-pdf/library/items/WAR8QI3Q?page=2&annotation=U4H7VI8S)

-  Details of main results

![[AT17_P8I3BGT9.png]] [(Alexeev and Thompson, 2019, p. 2)](zotero://open-pdf/library/items/WAR8QI3Q?page=2&annotation=6TL9KJ97)

![[AT17_R59S78ZZ.png]] [(Alexeev and Thompson, 2019, p. 9)](zotero://open-pdf/library/items/WAR8QI3Q?page=9&annotation=3XNAMCMC)

![[AT17_AXHXGSQX.png]] [(Alexeev and Thompson, 2019, p. 10)](zotero://open-pdf/library/items/WAR8QI3Q?page=10&annotation=QFULQUCC)