# Multidimensional residues and ideal membership.

Publicacions Matemàtiques (1998)

- Volume: 42, Issue: 1, page 143-152
- ISSN: 0214-1493

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topPerotti, Alessandro. "Multidimensional residues and ideal membership.." Publicacions Matemàtiques 42.1 (1998): 143-152. <http://eudml.org/doc/41331>.

@article{Perotti1998,

abstract = {Let I(f) be a zero-dimensional ideal in C[z1, ..., zn] defined by a mapping f. We compute the logarithmic residue of a polynomial g with respect to f. We adapt an idea introduced by Aizenberg to reduce the computation to a special case by means of a limiting process.We then consider the total sum of local residues of g w.r.t. f. If the zeroes of f are simple, this sum can be computed from a finite number of logarithmic residues. In the general case, you have to perturb the mapping f. Some applications are given. In particular, the global residue gives, for any polynomial, a canonical representative in the quotient space C[z]/I(f).},

author = {Perotti, Alessandro},

journal = {Publicacions Matemàtiques},

keywords = {Funciones de variable compleja; Funciones de varias variables; Funciones holomorfas de varias variables; Residuos; integral representations; multidimensional residues; local residues},

language = {eng},

number = {1},

pages = {143-152},

title = {Multidimensional residues and ideal membership.},

url = {http://eudml.org/doc/41331},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Perotti, Alessandro

TI - Multidimensional residues and ideal membership.

JO - Publicacions Matemàtiques

PY - 1998

VL - 42

IS - 1

SP - 143

EP - 152

AB - Let I(f) be a zero-dimensional ideal in C[z1, ..., zn] defined by a mapping f. We compute the logarithmic residue of a polynomial g with respect to f. We adapt an idea introduced by Aizenberg to reduce the computation to a special case by means of a limiting process.We then consider the total sum of local residues of g w.r.t. f. If the zeroes of f are simple, this sum can be computed from a finite number of logarithmic residues. In the general case, you have to perturb the mapping f. Some applications are given. In particular, the global residue gives, for any polynomial, a canonical representative in the quotient space C[z]/I(f).

LA - eng

KW - Funciones de variable compleja; Funciones de varias variables; Funciones holomorfas de varias variables; Residuos; integral representations; multidimensional residues; local residues

UR - http://eudml.org/doc/41331

ER -

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