Singularities of logarithmic foliations

[摘要] A logarithmic 1-form on $mathbb Cmathbb P^n$ can be written asomega=iggl(prod_0^m F_jiggr)sum_0^m lambda_ifrac{dF_i}{F_i}=lambda_0 widehat F_0 ,dF_0+cdots+lambda_m widehat F_m ,dF_mwith $widehat F_i=(prod_0^m F_j)/F_i$ for some homogeneous polynomials Fi of degree di and constants $lambda_iin{mathbb C}^star$ such that $sumlambda_id_i=0$. For general $F_i,lambda_i$, the singularities of $omega$ consist of a schematic union of the codimension 2 subvarieties Fi = Fj = 0 together with, possibly, finitely many isolated points. This is the case when all Fi are smooth and in general position. In this situation, we give a formula which prescribes the number of isolated singularities.

[学科分类] 数学（综合）