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arXiv · 2409.14404

Singularity formation in co-dimension one of the dHYM cotangent flow on blow up of $\mathbb{C}\mathbb{P}^{3}$ at a point

Ramesh Mete
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Abstract

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 K\"{a}hler 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.

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Ramesh Mete. 2024-09-22. Singularity formation in co-dimension one of the dHYM cotangent flow on blow up of $\mathbb{C}\mathbb{P}^{3}$ at a point. https://doi.org/10.4310/mrl.260502194947

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