LitNote-Alexeev and Thompson-2019-ADE surfaces and their moduli-AT17

- 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



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.

Extracted Annotations

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

  • Defining the moduli space of (weighted) stable curves

File:AT17_HS9VRP3I.png (Alexeev and Thompson, 2019, p. 2)

  • Context (some motivating results)

File:AT17_WSSMNSQN.png (Alexeev and Thompson, 2019, p. 2)

  • Main result of this paper.

File:AT17_EYEZ8H4F.png (Alexeev and Thompson, 2019, p. 2)

  • Definition of surface pairs.

File:AT17_TVNDPLQE.png (Alexeev and Thompson, 2019, p. 2)

  • Details of main results

File:AT17_P8I3BGT9.png (Alexeev and Thompson, 2019, p. 2)

File:AT17_R59S78ZZ.png (Alexeev and Thompson, 2019, p. 9)

File:AT17_AXHXGSQX.png (Alexeev and Thompson, 2019, p. 10)