# Divisors in global analytic sets

Francesca Acquistapace; A. Díaz-Cano

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 2, page 297-307
- ISSN: 1435-9855

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topAcquistapace, Francesca, and Díaz-Cano, A.. "Divisors in global analytic sets." Journal of the European Mathematical Society 013.2 (2011): 297-307. <http://eudml.org/doc/277592>.

@article{Acquistapace2011,

abstract = {We prove that any divisor $Y$ of a global analytic set $X \subset \mathbb \{R\}^n$ has a generic equation, that is, there is an analytic function vanishing on $Y$ with multiplicity one along each irreducible component of $Y$. We also prove that there are functions with arbitrary multiplicities along $Y$. The main result states that if $X$ is pure dimensional, $Y$ is locally principal, $X/Y$ is not connected and $Y$ represents the zero class in $H^\infty _\{q-1\}(X,\mathbb \{Z\}_2)$ then the divisor $Y$ is globally principal.},

author = {Acquistapace, Francesca, Díaz-Cano, A.},

journal = {Journal of the European Mathematical Society},

keywords = {real analytic sets; divisors; real analytic set; divisor},

language = {eng},

number = {2},

pages = {297-307},

publisher = {European Mathematical Society Publishing House},

title = {Divisors in global analytic sets},

url = {http://eudml.org/doc/277592},

volume = {013},

year = {2011},

}

TY - JOUR

AU - Acquistapace, Francesca

AU - Díaz-Cano, A.

TI - Divisors in global analytic sets

JO - Journal of the European Mathematical Society

PY - 2011

PB - European Mathematical Society Publishing House

VL - 013

IS - 2

SP - 297

EP - 307

AB - We prove that any divisor $Y$ of a global analytic set $X \subset \mathbb {R}^n$ has a generic equation, that is, there is an analytic function vanishing on $Y$ with multiplicity one along each irreducible component of $Y$. We also prove that there are functions with arbitrary multiplicities along $Y$. The main result states that if $X$ is pure dimensional, $Y$ is locally principal, $X/Y$ is not connected and $Y$ represents the zero class in $H^\infty _{q-1}(X,\mathbb {Z}_2)$ then the divisor $Y$ is globally principal.

LA - eng

KW - real analytic sets; divisors; real analytic set; divisor

UR - http://eudml.org/doc/277592

ER -

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