# Normal bundles on the exceptional sets of simple small resolutions

## TL;DR

This paper investigates the structure of normal bundles on exceptional sets of certain singularities in higher dimensions, extending classical results to more complex cases with specific geometric conditions.

## Contribution

It generalizes Nakayama, Ando, and Laufer's results to higher dimensions under specific conditions on the exceptional set and its normal bundle.

## Key findings

- Extended Nakayama and Ando's results to higher dimensions.
- Generalized Laufer's rationality and embedding dimension results.
- Analyzed normal bundles with good filtrations on exceptional sets.

## Abstract

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 Ando's results to higher dimension. Moreover, we also generalize Laufer's results of rationality and embedding dimension to higher dimension.