On properness of K-moduli spaces and optimal degenerations of Fano varieties
Abstract We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable Fano varieties. Specifically, we prove that if the stability threshold of every K-unstable Fano...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2021
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| Online Access: | https://hdl.handle.net/1721.1/136911 |
| _version_ | 1826210054968180736 |
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| author | Blum, Harold Halpern-Leistner, Daniel Liu, Yuchen Xu, Chenyang |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Blum, Harold Halpern-Leistner, Daniel Liu, Yuchen Xu, Chenyang |
| author_sort | Blum, Harold |
| collection | MIT |
| description | Abstract
We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable Fano varieties. Specifically, we prove that if the stability threshold of every K-unstable Fano variety is computed by a divisorial valuation, then such K-moduli spaces are proper. The argument relies on studying certain optimal destabilizing test configurations and constructing a
$$\Theta $$
Θ
-stratification on the moduli stack of Fano varieties. |
| first_indexed | 2024-09-23T14:41:06Z |
| format | Article |
| id | mit-1721.1/136911 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:41:06Z |
| publishDate | 2021 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1369112023-12-13T15:38:53Z On properness of K-moduli spaces and optimal degenerations of Fano varieties Blum, Harold Halpern-Leistner, Daniel Liu, Yuchen Xu, Chenyang Massachusetts Institute of Technology. Department of Mathematics Abstract We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable Fano varieties. Specifically, we prove that if the stability threshold of every K-unstable Fano variety is computed by a divisorial valuation, then such K-moduli spaces are proper. The argument relies on studying certain optimal destabilizing test configurations and constructing a $$\Theta $$ Θ -stratification on the moduli stack of Fano varieties. 2021-11-01T14:34:09Z 2021-11-01T14:34:09Z 2021-07-28 2021-07-29T03:19:16Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136911 Selecta Mathematica. 2021 Jul 28;27(4):73 en https://doi.org/10.1007/s00029-021-00694-7 Creative Commons Attribution-Noncommercial-Share Alike https://creativecommons.org/licenses/by/4.0/ The Author(s), under exclusive licence to Springer Nature Switzerland AG application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Blum, Harold Halpern-Leistner, Daniel Liu, Yuchen Xu, Chenyang On properness of K-moduli spaces and optimal degenerations of Fano varieties |
| title | On properness of K-moduli spaces and optimal degenerations of Fano varieties |
| title_full | On properness of K-moduli spaces and optimal degenerations of Fano varieties |
| title_fullStr | On properness of K-moduli spaces and optimal degenerations of Fano varieties |
| title_full_unstemmed | On properness of K-moduli spaces and optimal degenerations of Fano varieties |
| title_short | On properness of K-moduli spaces and optimal degenerations of Fano varieties |
| title_sort | on properness of k moduli spaces and optimal degenerations of fano varieties |
| url | https://hdl.handle.net/1721.1/136911 |
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