Resolution of singularities of threefolds in positive characteristic I
V Cossart, O Piltant - Journal of Algebra, 2008 - hal.science
The purpose of this article and of" Resolution of singularities of threefolds in positive
characteristic II" is to prove the theorem of resolution: resolution of singularities holds for …
characteristic II" is to prove the theorem of resolution: resolution of singularities holds for …
[图书][B] Resolution of singularities
SD Cutkosky - 2004 - books.google.com
The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of
singularities by simple algebraic mappings is truly a fundamental problem. It has a complete …
singularities by simple algebraic mappings is truly a fundamental problem. It has a complete …
Valuations, deformations, and toric geometry
B Teissier - arXiv preprint math/0303200, 2003 - arxiv.org
A study of the relation between a noetherian local domain with a given valuation and its
associated graded ring with respect to the valuation, which in some cases is an esentially …
associated graded ring with respect to the valuation, which in some cases is an esentially …
Value groups, residue fields, and bad places of rational function fields
FV Kuhlmann - Transactions of the American Mathematical Society, 2004 - ams.org
We classify all possible extensions of a valuation from a ground field $ K $ to a rational
function field in one or several variables over $ K $. We determine which value groups and …
function field in one or several variables over $ K $. We determine which value groups and …
Overweight deformations of affine toric varieties and local uniformization
B Teissier - arXiv preprint arXiv:1401.5204, 2014 - arxiv.org
We study Abhyankar valuations of excellent equicharacteristic local domains with an
algebraically closed residue field. For zero dimensional valuations we prove that whenever …
algebraically closed residue field. For zero dimensional valuations we prove that whenever …
A classification of Artin–Schreier defect extensions and characterizations of defectless fields
FV Kuhlmann - Illinois Journal of Mathematics, 2010 - projecteuclid.org
We classify Artin–Schreier extensions of valued fields with nontrivial defect according to
whether they are connected with purely inseparable extensions with nontrivial defect, or not …
whether they are connected with purely inseparable extensions with nontrivial defect, or not …
The defect
FV Kuhlmann - Commutative Algebra: Noetherian and Non-Noetherian …, 2010 - Springer
This work was partially supported by a Canadian NSERC grant and by a sabbatical grant
from the University of Saskatchewan. I thank Bernard Teissier, Olivier Piltant, Michael …
from the University of Saskatchewan. I thank Bernard Teissier, Olivier Piltant, Michael …
[图书][B] Monomialization of morphisms from 3-folds to surfaces
SD Cutkosky - 2002 - books.google.com
A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally
be represented in e'tale neighborhoods by a pure monomial mappings. The book gives …
be represented in e'tale neighborhoods by a pure monomial mappings. The book gives …
Defect and local uniformization
SD Cutkosky, H Mourtada - Revista de la Real Academia de Ciencias …, 2019 - Springer
We give a simple algorithm showing that the reduction of the multiplicity of a characteristic
p> 0 p> 0 hypersurface singularity along a valuation is possible if there is a finite linear …
p> 0 p> 0 hypersurface singularity along a valuation is possible if there is a finite linear …
The valuation theory of deeply ramified fields and its connection with defect extensions
FV Kuhlmann, A Rzepka - Transactions of the American Mathematical …, 2023 - ams.org
We study in detail the valuation theory of deeply ramified fields and introduce and
investigate several other related classes of valued fields. Further, a classification of defect …
investigate several other related classes of valued fields. Further, a classification of defect …