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The perfect cone compactification of quotients of type IV domains

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posted on 24.01.2022, 09:19 authored by Luca GiovenzanaLuca Giovenzana
Abstract. The perfect cone compactification is a toroidal compactification which can be defined for locally symmetric varieties. Let DL/Õ+(L)p be the perfect cone compactification of the quotient of the type IV domain DL associated to an even lattice L. In our main theorem we show that the pair (DL/Õ+(L)p , ∆/2) has klt singularities, where ∆ is the closure of the branch divisor of DL/Õ+(L)p.
In particular this applies to the perfect cone compactification of the moduli space of 2d-polarised K3 surfaces with ADE singularities when d is square-free.

Funding

DFG through the research grant Le 3093/3-1

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School

  • Science

Department

  • Mathematical Sciences

Published in

Manuscripta Mathematica

Publisher

Springer Verlag

Version

VoR (Version of Record)

Rights holder

© the Authors

Publisher statement

This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

Acceptance date

09/11/2021

Publication date

2021-12-27

ISSN

0025-2611

eISSN

1432-1785

Language

en

Depositor

Luca Giovenzana. Deposit date: 13 December 2021

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