A note on the Nielsen realization problem for hyper-Kähler manifolds

被引：0

作者：

Simone Billi ^{[1
]}

机构：

[1] University of Genova,Department of Mathematics

来源：

Geometriae Dedicata | 2025年 / 219卷 / 3期

关键词：

Hyperkähler; Mapping class group; Nielsen realization problem; Teichmüller space; 14J42; 53C26; 32Q20;

D O I：

10.1007/s10711-025-01007-4

中图分类号：

学科分类号：

摘要：

We give an answer to the Nielsen realization problem for hyper-Kähler manifolds in analogy to the case of K3 surfaces. We determine that, for some of the known deformation types, the representation of the mapping class group on the second cohomology admits a section on its image.

引用

共 6 条

[1] The Nielsen realization problem for non-orientable surfaces
Colin, Nestor
Xicotencatl, Miguel A.
TOPOLOGY AND ITS APPLICATIONS, 2024, 353
[2] THE NIELSEN REALIZATION PROBLEM FOR ASYMPTOTIC TEICHMULLER MODULAR GROUPS
Fujikawa, Ege
Matsuzaki, Katsuhiko
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 365 (06) : 3309 - 3327
[3] The Nielsen realization problem for high degree del Pezzo surfaces
Lee, Seraphina Eun Bi
GEOMETRIAE DEDICATA, 2024, 218 (03)
[4] Abelianization and Nielsen realization problem of the mapping class group of a handlebody
Hirose, Susumu
GEOMETRIAE DEDICATA, 2012, 157 (01) : 217 - 225
[5] Abelianization and Nielsen realization problem of the mapping class group of a handlebody
Susumu Hirose
Geometriae Dedicata, 2012, 157 : 217 - 225
[6] The diffeomorphism group of a K3 surface and Nielsen realization
Giansiracusa, Jeffrey
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2009, 79 : 701 - 718

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