Disentangling mappings defined on ICIS

Abstract

Let $(X,S)$ be an isolated complete intersection singularity of dimension $n$, and let $f:(X,S)\rightarrow (\mathbb{C}^{n+1},0)$ be a germ of $\mathscr{A}$-finite mapping. In this master's degree final project, our main contribution is that we show the case $n=2$ of the general Mond conjecture, which states that $μ_I(X,f)\geq \text{codim}_{\mathscr{A}_e}(X,f)$, with equality provided $(X,f)$ is weighted homogeneous. Before this project, the only known case for which the conjecture was known to hold is in the case that $n=1$ and $(X,S)$ is a plane curve.

Figures (5)

• Figure 1: Representation of a mapping $f$ defined on an icis$X$, and its image $f(X)$. Image extracted from the article roberto by R. Giménez Conejero and J.J. Nuño-Ballesteros.
• Figure 2: Real picture of the space $\mathfrak{X}$ in the example \ref{['example:unfolding']}. The red fibre in the middle corresponds to $X=\pi^{-1}(0)$ and the other ones correspond to $\pi^{-1}(-1)$ and $\pi^{-1}(1)$.
• Figure 3: Representation of the disentanglement of a mapping defined on an ICIS. Image extracted from the article roberto by R. Giménez Conejero and J.J. Nuño-Ballesteros.
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Theorems & Definitions (161)

• Definition 1.1
• Remark 1.2
• Definition 1.3
• Definition 1.4
• Definition 1.5
• Remark 1.6
• Definition 1.7
• Remark 1.8
• Theorem 1.9
• proof