Singular Gauduchon Conjecture
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908728809226240 |
|---|---|
| author | Cerqueira-Gonçalves, Guilherme |
| author_facet | Cerqueira-Gonçalves, Guilherme |
| contents | In 1984 Gauduchon conjectured that one can find Gauduchon metrics with prescribed Ricci curvature on all compact complex manifolds. This conjecture was settled by Székelyhidi-Tosatti-Weinkove (TW17, TW19, STW17) by the study of the Monge-Ampère equation for $(n-1)$-plurisubharmonic functions with a gradient term. In this paper we study a singular version of this conjecture. We obtain a $C^{0}$-estimate for this problem, without gradient terms, in smoothable hermitian variaties by adapting a recent technique of Guedj-Lu. We also prove the smoothness of solutions on holomorphic Kähler families, generalizing TW17. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular Gauduchon Conjecture Cerqueira-Gonçalves, Guilherme Differential Geometry Complex Variables In 1984 Gauduchon conjectured that one can find Gauduchon metrics with prescribed Ricci curvature on all compact complex manifolds. This conjecture was settled by Székelyhidi-Tosatti-Weinkove (TW17, TW19, STW17) by the study of the Monge-Ampère equation for $(n-1)$-plurisubharmonic functions with a gradient term. In this paper we study a singular version of this conjecture. We obtain a $C^{0}$-estimate for this problem, without gradient terms, in smoothable hermitian variaties by adapting a recent technique of Guedj-Lu. We also prove the smoothness of solutions on holomorphic Kähler families, generalizing TW17. |
| title | Singular Gauduchon Conjecture |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2512.19830 |