Saved in:
Bibliographic Details
Main Authors: Deng, Fusheng, Li, Yinji, Liu, Qunhuan, Zhou, Xiangyu
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2409.09402
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • We prove that the irreducible desingularization of a singularity given by the Grauert blow down of a negative holomorphic vector bundle over a compact complex manifold is unique up to isomorphism, and as an application, we show that two negative line bundles over compact complex manifolds are isomorphic if and only if their Grauert blow downs have isomorphic germs near the singularities. We also show that there is a unique way to modify a submanifold of a complex manifold to a hypersurface, namely, the blow up of the ambient manifold along the submanifold.