Asian Journal of Mathematics

Volume 25 (2021)

Number 2

Normal bundles on the exceptional sets of simple small resolutions

Pages: 295 – 304



Rong Du (School of Mathematical Sciences, Shanghai Key Laboratory, East China Normal University, Shanghai, China)

Xinyi Fang (Department of Mathematics, Nanjing University, Nanjing, China)


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

14B05, 14J60

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