Uniqueness of irreducible desingularization of singularities arising from blow down negative vector bundles
Prof. Fusheng Deng
2024-07-01 14:00-15:00
MCM110
Speaker: Prof. Fusheng Deng (University of Chinese Academy of Sciences)Time: 14:00-15:00 July 1, 2024 (Monday)
Venue: MCM110
Title: Uniqueness of irreducible desingularization of singularities arising from blow downs of negative vector bundles
Abstract: 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. This is joint with Yinji Li, Qunhuan Liu, and Xiangyu Zhou.
