ADE surfaces and their moduli
Algebraic Geometry
2019-10-08 v3 Representation Theory
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.
Cite
@article{arxiv.1712.07932,
title = {ADE surfaces and their moduli},
author = {Valery Alexeev and Alan Thompson},
journal= {arXiv preprint arXiv:1712.07932},
year = {2019}
}
Comments
A streamlined and expanded version