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arXiv · 1712.07932

ADE surfaces and their moduli

Valery Alexeev·Alan Thompson
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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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Valery Alexeev, Alan Thompson. 2017-12-21. ADE surfaces and their moduli. https://arxiv.org/abs/1712.07932

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