Bouquet decomposition for determinantal Milnor fibers

TL;DR

This paper introduces a bouquet decomposition method for determinantal Milnor fibers of isolated singularities, using hyperplane sections of generic determinantal varieties to analyze their structure.

Contribution

It provides a novel bouquet decomposition framework for determinantal Milnor fibers of arbitrary type, expanding understanding of their topological structure.

Findings

Decomposition into suspensions of hyperplane sections

Applicable to arbitrary determinantal singularity types

Enhances topological analysis of Milnor fibers

Abstract

We provide a bouquet decomposition for the determinantal Milnor fiber of an essentially isolated determinantal singularity of arbitrary type $(m,n,t)$. The building blocks in the decomposition are (suspensions of) hyperplane sections of the associated generic determinantal variety $M_{m,n}^t$ in general position off the origin.