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Guillermo Peñafort Sanchis

Publications and source records attributed to Guillermo Peñafort Sanchis.

6 recordsLinked to original sources
arXiv2025

Lipschitz geometry of the image of finite mappings

This paper is devoted to the study of the LNE property in complex analytic hypersurface parametrized germs, that is, the sets that are images of finite analytic map germs from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$. We prove that if the multiplicity of $f$ is equal to his generic degree, then the image of $f$ is LNE at 0 if and only if it is a smooth germ. We also show that every finite corank 1 map is sattisfies the previous hypothesis. Moreover, we show that for an injective map germ $f$ from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$, the image of $f$ is LNE at 0 if and only if $f$ is an embedding.

math.AG↗
arXiv2024

On the analytic structure of double and triple points in the target of finite holomorphic multi-germs

We study the analytic structure of the double and triple point spaces $M_2(f)$ and $M_3(f)$ of finite multi-germs $f\colon (X,S)\to(\mathbb{C}^{n+1},0)$, based on results of Mond and Pellikaan for the mono-germ case. We show that these spaces are Cohen-Macaulay, provided that certain dimensional conditions are satisfied, and give explicit expressions for their defining ideals in terms of those of their mono-germ branches.

math.AG↗
arXiv2021

Cohomological connectivity of perturbations of map-germs

Let $f\colon (\mathbb C^n,S)\to (\mathbb C^p,0)$ be a finite map-germ with $n<p$ and $Y_δ$ the image of a small perturbation $f_δ$. We show that the reduced cohomology of $Y_δ$ is concentrated in a range of degrees determined by the dimension of the instability locus of $f$. In the case $n\geq p$ we obtain an analogous result, replacing finiteness by $\mathcal K$-finiteness and $Y_δ$ by the discriminant $Δ(f_δ)$. We also study the monodromy associated to the perturbation $f_δ$.

math.AG↗
arXiv2020

Image Milnor number formulas for weighted-homogeneous map-germs

We give formulas for the image Milnor number of a weighted-homogeneous map-germ $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely interpolative method, applied to a result by Ohmoto. We use our approach to recover the formulas for $n=2$ and $3$ due to Mond and Ohmoto, respectively. For $n\geq 6$, the method is valid as long as certain multi-singularity conjecture holds.

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arXiv2019

Kato-Matsumoto-type results for disentanglements

We consider the possible disentanglements of holomorphic map germs $f \colon (\mathbb C^n,0) \to (\mathbb C^N,0)$, $n < N$, with nonisolated locus of instability $\operatorname{Inst}(f)$. The aim is to achieve lower bounds for their (homological) connectivity in terms of $\dim \operatorname{Inst}(f)$. Our methods apply in the case of corank $1$.

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