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.

引用

页码：375 / 386

页数：12

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