5 citations · 6 across the 9 of their papers we have counts for
16 papers
Desingularization of generic symmetric and generic skew-symmetric determinantal singularities
Sabrina Alexandra Gaube, Bernd Schober
We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order t…
Constancy of the Hilbert-Samuel function
Vincent Cossart, Olivier Piltant, Bernd Schober
The Hilbert-Samuel function and the multiplicity function are fundamental locally defined invariants on Noetherian schemes. They have been playing an important role in desingulariz…
Desingularization of binomial varieties using toric Artin stacks
Dan Abramovich, Bernd Schober
We show how the notion of fantastacks can be used to effectively desingularize binomial varieties defined over algebraically closed fields. In contrast to a desingularization via b…
Classification of singularities of cluster algebras of finite type: the case of trivial coefficients
Angelica Benito, Eleonore Faber, Hussein Mourtada +1
We provide a complete classification of the singularities of cluster algebras of finite type with trivial coefficients. Alongside, we develop a constructive desingularization of th…
Algorithmic local monomialization of a binomial: a comparison of different approaches
Sabrina Alexandra Gaube, Bernd Schober
We investigate different approaches to transform a given binomial into a monomial via blowing up appropriate centers. In particular, we develop explicit implementations in {\sc Sin…
Loose edges and factorization theorems
Janusz Gwoździewicz, Beata Hejmej, Bernd Schober
Let be a regular local ring with maximal ideal . We consider elements such that their Newton polyhedron has a loose edge. We show that if the symb…
Generalized Loose Edge Factorization Theorems
Bernd Schober
We extend a factorization theorem by Gwoździewicz and Hejmej from the ring of formal power series to any complete regular local ring . More precisely, let and assu…
Invariance of Hironaka's characteristic polyhedron
Vincent Cossart, Uwe Jannsen, Bernd Schober
We show that given a face of Hironaka's characteristic polyhedron, it does only depend on the singularity and a flag defined by the linear form determining the face. As a consequen…
Embedded desingularization for arithmetic surfaces -- toward a parallel implementation
Anne Fruehbis-Krueger, Lukas Ristau, Bernd Schober
We present an algorithmic embedded desingularization of arithmetic surfaces bearing in mind implementability. Our algorithm is based on work by Cossart-Jannsen-Saito, though our va…
Partial local resolution by characteristic zero methods
Bernd Schober
We discuss to what extent the local techniques of resolution of singularities over fields of characteristic zero can be applied to improve singularities in general. For certain int…
An irreducibility criterion for power series
Guillaume Rond, Bernd Schober
We prove an irreducibility criterion for polynomials with power series coefficients generalizing previous known results concerning quasi-ordinary polynomials.
A polyhedral characterization of quasi-ordinary singularities
Hussein Mourtada, Bernd Schober
Given an irreducible hypersurface singularity of dimension (defined by a polynomial ) and the projection to the affine space defined by …
A strictly decreasing invariant for resolution of singularities in dimension two
Vincent Cossart, Bernd Schober
We construct a local invariant for resolution of singularities of 2-dimensional excellent Noetherian schemes with boundary. We prove that the invariant strictly decreases at every…
Characteristic polyhedra of singularities without completion -- Part II
Vincent Cossart, Bernd Schober
Hironaka's characteristic polyhedron is an important combinatorial object reflecting the local nature of a singularity. We prove that it can be determined without passing to the co…
A polyhedral approach to the invariant of Bierstone and Milman
Bernd Schober
Based on previous work by the author we deduce that the invariant introduced by Bierstone and Milman in order to give a proof for constructive resolution of singularities in charac…
Idealistic exponents: Tangent cone, ridge, characteristic polyhedra
Bernd Schober
We study Hironaka's idealistic exponents over . We give an idealistic interpretation of the tangent cone, the directrix, and the ridge. The ma…