与负向量丛相关的奇点的不可约消歧的唯一性
Uniqueness of irreducible desingularization of singularities associated to negative vector bundles
AI总结：
本文证明紧复流形上负全纯向量丛经 Grauert 向下爆破所得奇点的不可约消歧唯一，并据此刻画负线丛同构及子流形到超曲面的唯一修改方式。
摘要：
我们证明了：由紧复流形上负全纯向量丛的 Grauert 向下爆破给出的奇点，其不可约消歧在同构意义下是唯一的。作为应用，我们表明，紧复流形上的两个负线丛同构，当且仅当它们的 Grauert 向下爆破在奇点附近具有同构的芽。我们还表明，将复流形的一个子流形修改为超曲面只有唯一一种方式，即沿该子流形对环境流形进行爆破。
英文摘要：
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.
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