Multiplicity of the Dual Variety
Multiplicity of the Dual Variety
复制标题
双品种的多重性
DOI：
10.1112/blms/23.5.429
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发表时间：
1991
影响因子：
0.9
通讯作者：
A. Parusiński
中科院分区：
文献类型：
--
作者：
A. Parusiński
设M是连通紧致复流形，dimM= n.设s ∈ H（E）\0是M上全纯向量丛E的全纯截面，X表示s的零集.然后，我们定义数ii（M; X）（或仅n（X）），其中x（X）表示X的（拓扑）Euler-Poincare特征，并且f（M，E）是E的截面（即，横切于零截面的全纯截面）的非奇异零集所期望的Euler-Poincare特征，其可以根据E和M的Chern类c（E），c（M）表示为
Let M be a connected compact complex manifold and let dimM= n. Let s e H (E)\0 be a holomorphic section of a holomorphic vector bundle E over M, and let X denote the zero set of s. Then, we define the number ii {M; X)(or just n (X)) by where x (X) denotes the (topological) Euler-Poincare characteristic of X and/(M, E) is the Euler-Poincare characteristic expected for a nonsingular zero set of a section of E (that is, of a holomorphic section transverse to the zero section), which can be expressed in terms of Chern classes c (E), c (M) of E and M as