RESOLUTION OF SINGULARITIES OF THREEFOLDS IN POSITIVE CHARACTERISTIC II

Vincent Cossart (1) , Olivier Piltant (1)

1 LMV - Laboratoire de Mathématiques de Versailles

In this second article, we solve the local uniformization problem for a hypersurface threefold singularity $(X_0,x_0)$ with equation~: $$h:=X^p-X g^{p-1}+f , \eqno (1)$$ where $(S,m_s)$ is a regular local ring of dimension three essentially of finite type over the ground field $k$, $f , g \in m_S$. The ground field $k$ is differentially finite over a perfect field $k_0$ of characteristic $p>0$. This ends the proof of resolution of threefolds in positive characteristic

Mots clés: resolution; desingularization; positive characteristic

Domaines: Géométrie algébrique [math.AG]

Vincent Cossart, Olivier Piltant. RESOLUTION OF SINGULARITIES OF THREEFOLDS IN POSITIVE CHARACTERISTIC II. Journal of Algebra, 2009, 321 (7), pp.1836-1976. ⟨10.1016/j.jalgebra.2008.11.030⟩. ⟨hal-00139445v2⟩