The deformation multiplicity of a map germ with respect to a Boardman symbol

Bivià-Ausina, Carles; Nuño–Ballesteros, J. J.

doi:10.1017/s0308210500001244

Cited by 6 publications

(4 citation statements)

References 9 publications

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“…This is precisely Lemma 4.5. The following lemma, which appears in [2], can be obtained easily from results about Cohen-Macaulay modules (see [11] for details). Proof.…”

Section: The Double Point Ideal Sheafmentioning

confidence: 99%

Multiple point spaces of finite holomorphic maps

Nuño–Ballesteros

Sanchis

2016

The Quarterly Journal of Mathematics

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Given a finite holomorphic map f : X → Y between manifolds, we show that there exists a unique possible definition of kth multiple point space D k (f ) with the following properties: D k (f ) is a closed subspace of X k , D k (f ) is the closure of the set of strict k-multiple points when f is stable and D k (f ) is well behaved under deformations. Our construction coincides with Mond's double point space and Mond's kth multiple point space for corank one singularities. We also give some interesting properties of the double point space and prove that in many cases it can be computed as the zero locus of the quotient of ideals2000 Mathematics Subject Classification. Primary 32S05; Secondary 58K20, 32S30.

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“…This is precisely Lemma 4.5. The following lemma, which appears in [2], can be obtained easily from results about Cohen-Macaulay modules (see [11] for details). Proof.…”

Section: The Double Point Ideal Sheafmentioning

confidence: 99%

Multiple point spaces of finite holomorphic maps

Nuño–Ballesteros

Sanchis

2016

The Quarterly Journal of Mathematics

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“…Note that the Cohen-Macaulay property of LC(V ) holds only for hypersurfaces, see [4]. We need the following lemma (see [1], Lemma 6.1) to prove the Theorem 3.7. dF (x)).…”

Section: Resultsmentioning

confidence: 99%

“…In this note we study function germs f : (C n , 0) → (C, 0) under the equivalence relation that preserves the analytic variety (V, 0). We say that two germs f 1…”

Section: Preliminary Resultsmentioning

confidence: 99%

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Invariants of topological relative right equivalences

Ahmed¹,

Ruas²,

Tomazella³

2013

Math. Proc. Camb. Phil. Soc.

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Let (V, 0) be the germ of an analytic variety in C n and f an analytic function germ defined on V. For functions with isolated singularity on V, Bruce and Roberts introduced a generalization of the Milnor number of f, which we call Bruce-Roberts number, μ B R (V, f ). Like the Milnor number of f, this number shows some properties of f and V. In this paper we investigate algebraic and geometric characterizations of the constancy of the Bruce-Roberts number for families of functions with isolated singularities on V. We also discuss the topological invariance of the Bruce-Roberts number for families of quasihomogeneous functions defined on quasihomogeneous varieties. As application of the results, we prove a relative version of the Zariski multiplicity conjecture for quasihomogeneous varieties.

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The Euler obstruction of a function on a determinantal variety and on a curve

Ament

Nuño–Ballesteros

Oréfice-Okamoto

et al. 2016

Bull Braz Math Soc, New Series

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Given an analytic function germ f : (X, 0) → C on an isolated determinantal singularity or on a reduced curve, we present formulas relating the local Euler obstruction of f to the vanishing Euler characteristic of the fiber X ∩ f −1 (0) and to the Milnor number of f . Restricting ourselves to the case where X is a complete intersection, we obtain an easy way to calculate the local Euler obstruction of f as the difference between the dimension of two algebras.

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The deformation multiplicity of a map germ with respect to a Boardman symbol

Cited by 6 publications

References 9 publications

Multiple point spaces of finite holomorphic maps

Multiple point spaces of finite holomorphic maps

Invariants of topological relative right equivalences

The Euler obstruction of a function on a determinantal variety and on a curve

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