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arXiv · 2507.06604

A hyperk\"ahler metric on twisted cotangent bundles of the complex projective space

Takashi Hashimoto
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Abstract

We construct a hyperk\"ahler metric on twisted cotangent bundles of the complex projective space $\mathbb{CP}^n$ explicitly in terms of local coordinates. Note that the twisted cotangent bundles of $\mathbb{CP}^n$ are holomorphically isomorphic to complex semisimple coadjoint orbits of $\mathrm{SL}_{n+1}(\mathbb{C})$.

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Takashi Hashimoto. 2025-07-09. A hyperk\"ahler metric on twisted cotangent bundles of the complex projective space. https://arxiv.org/abs/2507.06604

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