Reductivity of the automorphism group of K-polystable Fano varieties
We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and Θ-reductivity of the moduli of K-semistable log Fano pairs. Assuming the conjecture that K-semistability is an open c...
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| מחברים אחרים: | |
| פורמט: | Article |
| שפה: | English |
| יצא לאור: |
Springer Berlin Heidelberg
2020
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| גישה מקוונת: | https://hdl.handle.net/1721.1/128467 |
| _version_ | 1826207687748091904 |
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| author | Alper, Jarod Blum, Harold Halpern-Leistner, Daniel Xu, Chenyang |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Alper, Jarod Blum, Harold Halpern-Leistner, Daniel Xu, Chenyang |
| author_sort | Alper, Jarod |
| collection | MIT |
| description | We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and Θ-reductivity of the moduli of K-semistable log Fano pairs. Assuming the conjecture that K-semistability is an open condition, we prove that the Artin stack parametrizing K-semistable Fano varieties admits a separated good moduli space. |
| first_indexed | 2024-09-23T13:53:24Z |
| format | Article |
| id | mit-1721.1/128467 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:53:24Z |
| publishDate | 2020 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1284672022-09-28T16:52:41Z Reductivity of the automorphism group of K-polystable Fano varieties Alper, Jarod Blum, Harold Halpern-Leistner, Daniel Xu, Chenyang Massachusetts Institute of Technology. Department of Mathematics We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and Θ-reductivity of the moduli of K-semistable log Fano pairs. Assuming the conjecture that K-semistability is an open condition, we prove that the Artin stack parametrizing K-semistable Fano varieties admits a separated good moduli space. NSF (Grants DMS-1440140, 11425101, DMS-1901849) 2020-11-12T21:48:38Z 2020-11-12T21:48:38Z 2020-07 2019-06 2020-10-30T04:34:37Z Article http://purl.org/eprint/type/JournalArticle 0020-9910 1432-1297 https://hdl.handle.net/1721.1/128467 Alper, Jarod et al. "Reductivity of the automorphism group of K-polystable Fano varieties." Inventiones mathematicae 220 (July 2020): 995–1032 © 2020 Springer-Verlag en https://doi.org/10.1007/s00222-020-00987-2 Inventiones mathematicae Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Alper, Jarod Blum, Harold Halpern-Leistner, Daniel Xu, Chenyang Reductivity of the automorphism group of K-polystable Fano varieties |
| title | Reductivity of the automorphism group of K-polystable Fano varieties |
| title_full | Reductivity of the automorphism group of K-polystable Fano varieties |
| title_fullStr | Reductivity of the automorphism group of K-polystable Fano varieties |
| title_full_unstemmed | Reductivity of the automorphism group of K-polystable Fano varieties |
| title_short | Reductivity of the automorphism group of K-polystable Fano varieties |
| title_sort | reductivity of the automorphism group of k polystable fano varieties |
| url | https://hdl.handle.net/1721.1/128467 |
| work_keys_str_mv | AT alperjarod reductivityoftheautomorphismgroupofkpolystablefanovarieties AT blumharold reductivityoftheautomorphismgroupofkpolystablefanovarieties AT halpernleistnerdaniel reductivityoftheautomorphismgroupofkpolystablefanovarieties AT xuchenyang reductivityoftheautomorphismgroupofkpolystablefanovarieties |