Canonical embedded and non-embedded resolution of singularities for excellent two-dimensional schemes - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2009

Canonical embedded and non-embedded resolution of singularities for excellent two-dimensional schemes

Résumé

We prove the existence of resolution of singularities for arbitrary (not necessarily reduced or irreducible) excellent two-dimensional schemes, via permissible blow-ups. The resolution is canonical, and functorial with respect to automorphisms or etale or Zariski localizations. We treat the embedded case as well as the non-embedded case, with or without a boundary, and we relate the diferent versions. In the non-embedded case, a boundary is a collection of locally principal closed subschemes. Our main tools are the stratifications by Hilbert-Samuel functions and the characteristic polyhedra introduced by H. Hironaka. In an appendix we show that the standard method used in characteristic zero - the theory of maximal contact - does not work for surfaces in positive characteristic (the counterexamples are hypersurfaces in affine threespace and work over any field of positive characteristic).

Dates et versions

hal-00672109 , version 1 (20-02-2012)

Identifiants

Citer

Vincent Cossart, Uwe Jannsen, Shuji Saito. Canonical embedded and non-embedded resolution of singularities for excellent two-dimensional schemes. 2009. ⟨hal-00672109⟩
85 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More