Linear components of the tangent cone in the Nash modification of a complex surface singularity

Snoussi, Jawad

doi:10.5427/jsing.2011.3e

Cited by 2 publications

(1 citation statement)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Example 3.4. We use for our purpose the following example due to J. Snoussi in [Sn2] of a surface singularity (X, 0) where the tangent cone has no linear component and the normalized Semple-Nash modification is a singular surface. We warn the reader that what follows requires some knowledge of resolution of singularities of surfaces.…”

Section: Ii)mentioning

confidence: 99%

Local polar varieties in the geometric study of singularities

Flores¹,

Teissier²

2018

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

View full text Add to dashboard Cite

This paper is dedicated to those administrators of research who realize how much damage is done by the evaluation of mathematical research solely by the rankings of the journals in which it is published, or more generally by bibliometric indices. We hope that their lucidity will become widespread in all countries. AbstractThis text presents several aspects of the theory of equisingularity of complex analytic spaces from the standpoint of Whitney conditions. The goal is to describe from the geometrical, topological, and algebraic viewpoints a canonical locally finite partition of a reduced complex analytic space X into nonsingular strata with the property that the local geometry of X is constant on each stratum. Local polar varieties appear in the title because they play a central role in the unification of viewpoints. The geometrical viewpoint leads to the study of spaces of limit directions at a given point of X ⊂ C n of hyperplanes of C n tangent to X at nonsingular points, which in turn leads to the realization that the Whitney conditions, which are used to define the stratification, are in fact of a Lagrangian nature. The local polar varieties are used to analyze the structure of the set of limit directions of tangent hyperplanes. This structure helps in particular to understand how a singularity differs from its tangent cone, assumed to be reduced. The multiplicities of local polar varieties are related to local topological invariants, local vanishing Euler-Poincaré characteristics, by a formula which turns out to contain, in the special case where the singularity is the vertex of the cone over a reduced projective variety, a Plücker-type formula for the degree of the dual of a projective variety. arXiv:1607.07979v3 [math.AG]

show abstract

Section: Ii)mentioning

confidence: 99%