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González Pérez, Pedro Daniel and GonzálezSprinberg, Gérard (2004) Analytical invariants of quasiordinary hypersurface singularities associated to divisorial valuations. Kodai Mathematical Journal, 27 (2). pp. 164173. ISSN 03865991

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Official URL: https://projecteuclid.org/euclid.kmj/1093351323
Abstract
Let (X, 0) be an irreducible germ of complex analytic space and b: (B,E) ! (X, 0) be its normalized blowup centered at 0 2 X, that is, the map obtained by first blowingup 0 on X and then normalizing the new space. To each irreducible component D of the exceptional divisor E is associated a divisorial valuation _D of K, the field of fractions of the local analytic algebra R of the germ (X, 0). Namely, if h 2 K, then _D(h) denotes the vanishing order of h _ b along D. The valuation _D defines a filtration of R by the ideals pk := {' 2 R _D(') _ k} for k _ 0 and an associated graded algebra grD(X, 0) := L k_0 pk/pk+1 with distinguished graded maximal ideal mD(X, 0) := L k_1 pk/pk+1. In this way, one obtains a finite set of pairs (grD(X, 0),mD(X, 0)), canonically associated to the analytic germ (X, 0).
Item Type:  Article 

Uncontrolled Keywords:  Surface singularities 
Subjects:  Sciences > Mathematics > Algebraic geometry 
ID Code:  12578 
Deposited On:  13 Apr 2011 08:47 
Last Modified:  14 May 2018 10:31 
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