# One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal

Open Mathematics (2011)

- Volume: 9, Issue: 6, page 1349-1353
- ISSN: 2391-5455

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topVeronique Lierde. "One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal." Open Mathematics 9.6 (2011): 1349-1353. <http://eudml.org/doc/268961>.

@article{VeroniqueLierde2011,

abstract = {Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate quadratic transform of R, if and only if the degree coefficient d(A v; v) is 1. We then give a criterion for R to be regular.},

author = {Veronique Lierde},

journal = {Open Mathematics},

keywords = {Degree function; Rees valuation; 2-dimensional rational singularity},

language = {eng},

number = {6},

pages = {1349-1353},

title = {One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal},

url = {http://eudml.org/doc/268961},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Veronique Lierde

TI - One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal

JO - Open Mathematics

PY - 2011

VL - 9

IS - 6

SP - 1349

EP - 1353

AB - Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate quadratic transform of R, if and only if the degree coefficient d(A v; v) is 1. We then give a criterion for R to be regular.

LA - eng

KW - Degree function; Rees valuation; 2-dimensional rational singularity

UR - http://eudml.org/doc/268961

ER -

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