Asian Journal of Mathematics
Volume 25 (2021)
Normal bundles on the exceptional sets of simple small resolutions
Pages: 295 – 304
We study the normal bundles of the exceptional sets of higher dimensional isolated simple small singularities when the Picard groups of the exceptional sets are of rank one and their normal bundles have certain good filtrations. In particular, we prove numerical inequalities satisfied by normal bundles of exceptional sets. Moreover, we generalize Laufer’s results on rationality and embedding dimension of singularities to higher dimension.
normal bundle, small singularity, exceptional set, embedding dimension
2010 Mathematics Subject Classification
The authors’ research was sponsored by the National Natural Science Foundation of China (Grant No. 11531007), by the Natural Science Foundation of China and the Israel Science Foundation (Grant No. 11761141005), and by the Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000).
Received 17 October 2019
Accepted 11 August 2020
Published 15 October 2021