Zobrazeno 1 - 10
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pro vyhledávání: '"Zach, Matthias"'
Autor:
Zach, Matthias
We extend the circle of ideas from a previous paper on hypersurfaces to functions $f \colon (\mathbb C^n, 0) \to (\mathbb C^k, 0)$ with an isolated singularity in a stratified sense on an arbitrary, but fixed complex analytic germ $(X, 0)$. An extens
Externí odkaz:
http://arxiv.org/abs/2411.02682
Autor:
Brandhorst, Simon, Zach, Matthias
We explain how to use the computer algebra system OSCAR to find all elliptic fibrations (up to automorphism) on a given surface and compute their Weierstrass models. This is illustrated for Vinberg's most algebraic K3 surface, the unique K3 surface o
Externí odkaz:
http://arxiv.org/abs/2311.11766
Autor:
Zach, Matthias
We study the cohomology of the generic determinantal varieties $M_{m,n}^s = \{ \varphi \in \mathbb C^{m\times n} : \mathrm{rank} \varphi
Externí odkaz:
http://arxiv.org/abs/2107.01823
Autor:
Frühbis-Krüger, Anne, Zach, Matthias
We survey determinantal singularities, their deformations, and their topology. This class of singularities generalizes the well studied case of complete intersections in several different aspects, but exhibits a plethora of new phenomena such as for
Externí odkaz:
http://arxiv.org/abs/2106.04855
Let $f\colon (\mathbb C^n,S)\to (\mathbb C^p,0)$ be a finite map-germ with $n
Externí odkaz:
http://arxiv.org/abs/2103.14685
Autor:
Zach, Matthias
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 arbitrarily singular reduced complex analytic space $(X,0) \subset (\mathbb
Externí odkaz:
http://arxiv.org/abs/2002.04009
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) con
Externí odkaz:
http://arxiv.org/abs/1807.07183
Autor:
Zach, Matthias
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 associate
Externí odkaz:
http://arxiv.org/abs/1804.02220
Autor:
Zach, Matthias
Publikováno v:
Journal of the London Mathematical Society; Nov2024, Vol. 110 Issue 5, p1-46, 46p
Autor:
Zach, Matthias
Publikováno v:
Geom. Topol. 25 (2021) 2167-2194
We extend the results from the previous paper by A. Fr\"uhbis-Kr\"uger and the author [arXiv:1501.01915] to the vanishing topology of those singularities in the title. Studying the case of possibly non-isolated singularities in the Tjurina- transform
Externí odkaz:
http://arxiv.org/abs/1607.07527