A note on the plane curve singularities in positive characteristic

被引：0
|
作者：
Barroso, E. V. E. L. I. A. R. GARCiA [1 ]
Ploski, Arkadiusz [2 ]
机构：
[1] Univ La Laguna, Dept Matemat Estadist & IO, IMAULL, Apartado Correos 456, San Cristobal la Laguna 38200, Tenerife, Spain
[2] Kielce Univ Technol, Dept Math & Phys, Al 1000 PP7, PL-25314 Kielce, Poland
来源：
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE | 2024年 / 67卷 / 03期
关键词：
Milnor number; Newton polygon; non-degeneracy; NEWTON POLYGON;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given an algebroid plane curve f = 0 over an algebraically closed field of characteristic p >= 0 we consider the Milnor number mu (f), the delta invariant delta(f) and the number r(f) of its irreducible components. Put (sic)(f) = 2 delta(f)- r(f) + 1. If p = 0 then (sic)(f ) = mu (f) (the Milnor formula). If p > 0 mu (f ) is not an invariant and mu (f) plays the role of mu (f). Let Nf be the Newton polygon of f. We define the numbers mu (N-f) and r(N-f) which can be computed by explicit formulas. The aim of this note is to give a simple proof of the inequality (sic)(f)- mu (N-f) >= r(N-f )- r(f) >= 0 due to Boubakri, Greuel and Markwig. We also prove that mu (f) = mu (N-f) when f is non-degenerate.
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页码：375 / 386
页数：12
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