Irregular fibers of complex polynomials in two variables.

Arnaud Bodin

Revista Matemática Complutense (2004)

  • Volume: 17, Issue: 1, page 67-81
  • ISSN: 1139-1138

Abstract

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For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective, surjective. Particularly this morphism is an isomorphism if and only if the corresponding irregular value is regular at infinity. We apply these results to the study of vanishing and invariant cycles.

How to cite

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Bodin, Arnaud. "Irregular fibers of complex polynomials in two variables.." Revista Matemática Complutense 17.1 (2004): 67-81. <http://eudml.org/doc/44530>.

@article{Bodin2004,
abstract = {For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective, surjective. Particularly this morphism is an isomorphism if and only if the corresponding irregular value is regular at infinity. We apply these results to the study of vanishing and invariant cycles.},
author = {Bodin, Arnaud},
journal = {Revista Matemática Complutense},
keywords = {Fibras; Morfismos; Funciones polinómicas; Singularidades; irregular fibers; vanishing cycles; invariant cycles},
language = {eng},
number = {1},
pages = {67-81},
title = {Irregular fibers of complex polynomials in two variables.},
url = {http://eudml.org/doc/44530},
volume = {17},
year = {2004},
}

TY - JOUR
AU - Bodin, Arnaud
TI - Irregular fibers of complex polynomials in two variables.
JO - Revista Matemática Complutense
PY - 2004
VL - 17
IS - 1
SP - 67
EP - 81
AB - For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective, surjective. Particularly this morphism is an isomorphism if and only if the corresponding irregular value is regular at infinity. We apply these results to the study of vanishing and invariant cycles.
LA - eng
KW - Fibras; Morfismos; Funciones polinómicas; Singularidades; irregular fibers; vanishing cycles; invariant cycles
UR - http://eudml.org/doc/44530
ER -

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