Geodesic
Smooth arcs on algebraic varieties
Journal of Singularities, Tome 16 (2017), pp. 130-140

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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.
DOI : 10.5427/jsing.2017.16f
Classification : 14E18, 14B20, 32S05 
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     author = {David Bourqui and Julien Sebag},
     title = {Smooth arcs on algebraic varieties},
     journal = {Journal of Singularities},
     pages = {130--140},
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     year = {2017},
     doi = {10.5427/jsing.2017.16f},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2017.16f/}
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David Bourqui; Julien Sebag. Smooth arcs on algebraic varieties. Journal of Singularities, Tome 16 (2017), pp. 130-140. doi: 10.5427/jsing.2017.16f

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