ADE surfaces and their moduli

Author:

Alexeev Valery,Thompson Alan

Abstract

We define a class of surfaces corresponding to the A D E 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.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology,Algebra and Number Theory

Reference30 articles.

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