63 citations · 76 across the 4 of their papers we have counts for
8 papers
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…
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…
Resolution of Singularities of Arithmetical Threefolds II
Vincent Cossart, Olivier Piltant
We prove Grothendieck's Conjecture on Resolution of Singulari-ties for quasi-excellent schemes X of dimension three and of arbitrary characteristic. This applies in particular to X…
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…
Characteristic polyhedra of singularities without completion
Vincent Cossart, Olivier Piltant
Let be a regular local G-ring with regular system of parameters . We prove that the Hironaka characteristic polyhedron , $f \…
Dicritical divisors after S.S. Abhyankar et I. Luengo
Vincent Cossart, Mickaël Matusinski
In [AL11], S.S Abhyankar and I. Luengo introduce a new theory of dicritical divisors in the most general framework. Here we simplify and generalize their results (see Theorems 3.1…
Canonical embedded and non-embedded resolution of singularities for excellent two-dimensional schemes
Vincent Cossart, Uwe Jannsen, Shuji Saito
We prove the existence of resolution of singularities for arbitrary (not necessarily reduced or irreducible) excellent two-dimensional schemes, via permissible blow-ups. The resolu…