Normal bundles on the exceptional sets of simple small resolutions


Abstract in English

We study the normal bundles of the exceptional sets of isolated simple small singularities in the higher dimension when the Picard group of the exceptional set is $mathbb{Z}$ and the normal bundle of it has some good filtration. In particular, for the exceptional set is a projective space with the split normal bundle, we generalized Nakayama and Andos results to higher dimension. Moreover, we also generalize Laufers results of rationality and embedding dimension to higher dimension.

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