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Determination of Baum–Bott residues of higher codimensional foliations
Asian Journal of Mathematics ( IF 0.5 ) Pub Date : 2019-01-01 , DOI: 10.4310/ajm.2019.v23.n3.a8
Maurício Corrêa 1 , Fernando Lourenço 2
Affiliation  

Let $\mathscr{F}$ be a singular holomorphic foliation, of codimension $k$, on a complex compact manifold such that its singular set has codimension $\geq k+1$. In this work we determinate Baum-Bott residues for $\mathscr{F}$ with respect to homogeneous symmetric polynomials of degree $k+1$. We drop the Baum-Bott's generic hypothesis and we show that the residues can be expressed in terms of the Grothendieck residue of an one-dimensional foliation on a $(k+1)$-dimensional disc transversal to a $(k+1)$-codimensional component of the singular set of $\mathscr{F}$. Also, we show that Cenkl's algorithm for non-expected dimensional singularities holds dropping the Cenkl's regularity assumption.

中文翻译:

测定高维叶面的 Baum-Bott 残基

令 $\mathscr{F}$ 是一个复数紧流形上的单数全纯叶状体,其余维数为 $k$,使得它的奇异集具有余维数 $\geq k+1$。在这项工作中,我们确定了 $\mathscr{F}$ 相对于 $k+1$ 次齐次对称多项式的 Baum-Bott 残差。我们放弃了 Baum-Bott 的一般假设,我们证明了残差可以用 $(k+1)$ 维圆盘横向到 $(k+1) 上的一维叶面的 Grothendieck 残差表示$\mathscr{F}$ 奇异集的 $-coDimension 分量。此外,我们证明了 Cenkl 的非预期维奇点算法可以放弃 Cenkl 的规律性假设。
更新日期:2019-01-01
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