Arcs schemes, derivations and Lipman's theorem

Julien Sebag (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this article, we prove that a projective plane curve defined over a subfield k of C is smooth over k if and only if its associated arcs scheme is reduced.

Mots clés: Differential algebra; Algebraic geometry; Derivation module on varieties; Arcs scheme

Domaines: Géométrie algébrique [math.AG]

Julien Sebag. Arcs schemes, derivations and Lipman's theorem. Journal of Algebra, 2011, 347 (1), pp.173-183. ⟨10.1016/j.jalgebra.2011.08.018⟩. ⟨hal-00672094⟩