ADE surfaces and their moduli

Alexeev, Valery; Thompson, Alan

doi:10.1090/jag/762

Authors: Valery Alexeev and Alan Thompson
Journal: J. Algebraic Geom. 30 (2021), 331-405
DOI: https://doi.org/10.1090/jag/762
Published electronically: November 19, 2020
MathSciNet review: 4233185
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Abstract | References | Additional Information

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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Additional Information

Valery Alexeev
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
MR Author ID: 317826
Email: valery@uga.edu

Alan Thompson
Affiliation: Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom
MR Author ID: 1025267
ORCID: 0000-0003-1400-0098
Email: a.m.thompson@lboro.ac.uk

Received by editor(s): January 7, 2019
Received by editor(s) in revised form: October 6, 2019, and December 20, 2019
Published electronically: November 19, 2020
Additional Notes: The first author was partially supported by the NSF under DMS-1603604 and DMS-1902157.