Singularity formation in co-dimension one of the dHYM cotangent flow on blow up of $\mathbb{C}\mathbb{P}^{3}$ at a point
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911667878625280 |
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| author | Mete, Ramesh |
| author_facet | Mete, Ramesh |
| contents | The existence and uniqueness of canonical singular solutions of the J-equation and the deformed Hermitian Yang Mills (dHYM) equation was proved in \cite{DMS24} on compact Kähler surfaces. In this paper, we study the singularity formation of the dHYM cotangent flow on the one-point blow up of $\mathbb{C}\mathbb{P}^3$ using Calabi ansatz. In particular, we provide an explicit example where the flow develops a singularity along the exceptional divisor. Moreover, the limit satisfies corresponding singular dHYM equation in the sense of \cite{DMS24} and provides some evidence for Conjecture $1.12$ in \cite{DMS24} on this three-dimensional manifold with symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14404 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singularity formation in co-dimension one of the dHYM cotangent flow on blow up of $\mathbb{C}\mathbb{P}^{3}$ at a point Mete, Ramesh Differential Geometry 2020: 32Q15 (Primary), 53C55, 58J35, 35A21 (Secondary) The existence and uniqueness of canonical singular solutions of the J-equation and the deformed Hermitian Yang Mills (dHYM) equation was proved in \cite{DMS24} on compact Kähler surfaces. In this paper, we study the singularity formation of the dHYM cotangent flow on the one-point blow up of $\mathbb{C}\mathbb{P}^3$ using Calabi ansatz. In particular, we provide an explicit example where the flow develops a singularity along the exceptional divisor. Moreover, the limit satisfies corresponding singular dHYM equation in the sense of \cite{DMS24} and provides some evidence for Conjecture $1.12$ in \cite{DMS24} on this three-dimensional manifold with symmetry. |
| title | Singularity formation in co-dimension one of the dHYM cotangent flow on blow up of $\mathbb{C}\mathbb{P}^{3}$ at a point |
| topic | Differential Geometry 2020: 32Q15 (Primary), 53C55, 58J35, 35A21 (Secondary) |
| url | https://arxiv.org/abs/2409.14404 |