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ADE surfaces and their moduli

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journal contribution
posted on 10.02.2020, 11:05 by Valery Alexeev, Alan ThompsonAlan Thompson
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.

Funding

NSF under DMS-1603604 and DMS-1902157

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Algebraic Geometry

Volume

30

Pages

331 - 405

Publisher

American Mathematical Society with University Press

Version

AM (Accepted Manuscript)

Rights holder

© American Mathematical Society

Publisher statement

First published in the Journal of Algebraic Geometry in [volume and number, year], published by American Mathematical Society. © 2020 American Mathematical Society.

Acceptance date

06/02/2020

Publication date

2020-11-19

Copyright date

2020

Notes

A streamlined and expanded version

ISSN

1056-3911

eISSN

1534-7486

Language

en

Depositor

Dr Alan Thompson Deposit date: 10 February 2020

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