Smooth arcs on algebraic varieties

David Bourqui and Julien Sebag

Journal of Singularities
volume 16 (2017), 130-140

Received 14 May 2017.

DOI: 10.5427/jsing.2017.16f

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Abstract:

Let k be a field and V be a k-variety. We say that a rational arc \gamma in L_\infty(V)(k) is smooth if its formal neighborhood L_\infty(V)_\gamma is an infinite-dimensional formal disk. In this article, we prove that every rational arc \gamma in (L_\infty(V) \ L_\infty(V_{\sing}))(k) is smooth if and only if the formal branch containing \gamma is smooth.

Keywords:

Arc scheme, curve singularity, formal neighborhood

2010 Mathematical Subject Classification:

14E18, 14B20, 32S05

Author(s) information:

David Bourqui	Julien Sebag
Institut de recherche mathématique de Rennes	Institut de recherche mathématique de Rennes
UMR 6625 du CNRS	UMR 6625 du CNRS
Université de Rennes 1	Université de Rennes 1
Campus de Beaulieu	Campus de Beaulieu
35042 Rennes cedex (France)	35042 Rennes cedex (France)
email: david.bourqui@univ-rennes1.fr	email: julien.sebag@univ-rennes1.fr