INNER RATES OF FINITE MORPHISMS - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

INNER RATES OF FINITE MORPHISMS

Abstract

Let (X, 0) be a complex analytic surface germ embedded in (C n , 0) with an isolated singularity and Φ = (g, f) : (X, 0) −→ (C 2 , 0) be a finite morphism. We define a family of analytic invariants of the morphism Φ, called inner rates of Φ. By means of the inner rates we study the polar curve associated to the morphism Φ when fixing the topological data of the curve (gf) −1 (0) and the surface germ (X, 0), allowing to address a problem called polar exploration. We also use the inner rates to study the geometry of the Milnor fibers of a non constant holomorphic function f : (X, 0) −→ (C, 0). The main result is a formula which involves the inner rates and the polar curve alongside topological invariants of the surface germ (X, 0) and the curve (gf) −1 (0).
Fichier principal
Vignette du fichier
inner-rates-of-finite-morphisms.pdf (565.99 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03794997 , version 1 (03-10-2022)
hal-03794997 , version 2 (18-06-2023)
hal-03794997 , version 3 (29-06-2023)

Identifiers

  • HAL Id : hal-03794997 , version 3

Cite

Yenni Cherik. INNER RATES OF FINITE MORPHISMS. 2023. ⟨hal-03794997v3⟩

Collections

UNIV-AMU INSMI
171 View
56 Download

Share

Gmail Facebook Twitter LinkedIn More