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We describe Baily-Borel, toroidal, and geometric -- using the KSBA stable pairs -- compactifications of some moduli spaces of K3 surfaces with a nonsymplectic automorphism of order \(3\) and \(4\) for which the fixed locus of the automorphism contains a curve of genus \(\ge2\). For order \(3\), we treat all the maximal-dimensional such families. We show that the toroidal and the KSBA compactifications in these cases admit simple descriptions in terms of certain \(ADE\) root lattices.
Details
Subject
Identifier / keyword
Title
Compactifications of moduli spaces of K3 surfaces with a higher-order nonsymplectic automorphism
Author
arXiv.org; Ithaca
Publication year
2024
Publication date
Dec 15, 2024
Section
Mathematics
Source
arXiv.org
Place of publication
Ithaca
Country of publication
United States
University/institution
Cornell University Library arXiv.org
Publication subject
e-ISSN
2331-8422
Source type
Working Paper
Language of publication
English
Document type
Working Paper
Publication history
Online publication date
2024-12-17
Milestone dates
2024-12-15 (Submission v1)
Publication history
First posting date
17 Dec 2024
ProQuest document ID
3145906562
Document URL
https://www.proquest.com/working-papers/compactifications-moduli-spaces-k3-surfaces-with/docview/3145906562/se-2?accountid=208611
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Copyright
© 2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Last updated
2024-12-18
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