Revista Matemática Complutense

, Volume 27, Issue 2, pp 461–499 | Cite as

Analytic theory of curvettes and dicriticals

Article

Abstract

The geometric theory of pencils in a germ of a smooth complex surface has been studied by several authors and their properties strongly lie on the structure of the dicritical components of their resolution, whereas the strict transform of the general element of the pencil by the resolution can be seen as a union of the so-called curvettes. This theory can be interpreted as the study of ideals (with two generators) in the ring of complex convergent power series in two variables, which is a local regular ring of dimension 2. In this work, we study properties of curvettes and dicriticals in an arbitrary local regular ring of dimension 2 (without restrictions on its characteristic or the one of its residue field). All the results are stated in purely algebraic terms though the ideas come from geometry.

Keywords

Analytic Contact number Curvette Dicritical divisor 

Mathematics Subject Classification (2000)

Primary 14A05 

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Copyright information

© Universidad Complutense de Madrid 2014

Authors and Affiliations

  1. 1.Mathematics DepartmentPurdue UniversityWest LafayetteUSA
  2. 2.Departamento de Matemáticas-IUMAUniversidad de ZaragozaZaragozaSpain

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