Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution
- Over the past 2 decades, there has been much progress on the classification of symplectic linear quotient singularities V/G admitting a symplectic (equivalently, crepant) resolution of singularities. The classification is almost complete but there is an infinite series of groups in dimension 4—the symplectically primitive but complex imprimitive groups—and 10 exceptional groups up to dimension 10, for which it is still open. In this paper, we treat the remaining infinite series and prove that for all but possibly 39 cases there is no symplectic resolution. We thereby reduce the classification problem to finitely many open cases. We furthermore prove non-existence of a symplectic resolution for one exceptional group, leaving 39+9=48 open cases in total. We do not expect any of the remaining cases to admit a symplectic resolution.
Author: | Gwyn Bellamy, Johannes Schmitt, Ulrich Thiel |
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URN: | urn:nbn:de:hbz:386-kluedo-78579 |
DOI: | https://doi.org/10.1007/s00209-021-02793-9 |
ISSN: | 1432-1823 |
Parent Title (English): | Mathematische Zeitschrift |
Publisher: | Springer Nature - Springer |
Document Type: | Article |
Language of publication: | English |
Date of Publication (online): | 2024/03/21 |
Year of first Publication: | 2021 |
Publishing Institution: | Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau |
Date of the Publication (Server): | 2024/03/21 |
Issue: | 300 |
Page Number: | 21 |
First Page: | 661 |
Last Page: | 681 |
Source: | https://link.springer.com/article/10.1007/s00209-021-02793-9 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Collections: | Open-Access-Publikationsfonds |
Licence (German): | Zweitveröffentlichung |