M. Zach

activity

20182021

most citedCohomological connectivity of perturbations of map-germs

1 citations · 3 across the 3 of their papers we have counts for

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5 papers · 1 filter

math.AG2021★ 1 cited

On the topology of determinantal links

Matthias Zach

We study the cohomology of the generic determinantal varieties $M_{m, n}^{s} = {φ \in C^{m \times n} : rank φ < s}$ , their polar multiplicities, their sections $D_k \…

math.AG2021★ 1 cited

Determinantal Singularities

Anne Frühbis-Krüger, Matthias Zach

We survey determinantal singularities, their deformations, and their topology. This class of singularities generalizes the well studied case of complete intersections in several di…

math.AG2021★ 1 cited

Cohomological connectivity of perturbations of map-germs

Yongqiang Liu, Guillermo Peñafort Sanchis, Matthias Zach

Let $f : (C^{n}, S) \to (C^{p}, 0)$ 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…

math.AG2020

A generalization of Milnor's formula

Matthias Zach

We describe a generalization of Milnor's formula for the Milnor number of an isolated hypersurface singularity to the case of a function $f$ whose restriction $f ∣ (X, 0)$ to an arbit…

math.AG2018

Bouquet decomposition for determinantal Milnor fibers

Matthias Zach

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 d…