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We establish the general formalism for constructing metrics of Calabi–Yau (p+1)-folds in terms of that of a p-fold by adding a complex-line bundle. We present a few explicit low-lying examples. We further consider holomorphic linearization and obtain the six-dimensional analogue of the Gibbons–Hawking instanton. Whilst the Kähler potential for the Gibbons–Hawking instanton is given by the harmonic...
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