2013/04/30 by János Kollár, András Némethi, Kollár, János +1
Mathematics · #(Secondary) #14B05 (Primary) 32S05 #14E15 #14E16 #14E18 #14J17 #32S50 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:14B05 #msc:14E15 #msc:14E16 #msc:14E18 #msc:14J17 #msc:32S05 #msc:32S50
paper · pdf · doi:10.48550/arxiv.1304.7853
arxiv created 2013/06/20 · arxiv updated 2013/06/21
Let X be a complex analytic space. A short analytic arc is a holomorphic map of the closed unit disc to X such that only the origin is mapped to a singular point. In contrast with the space of formal arcs studied by Nash, the moduli space of short analytic arcs usually has infinitely many connected components. We describe these for surface singularities, in terms of certain conjugacy classes of the fundamental group of the link. For quotient singularities (in any dimension), this gives a concrete realization of the McKay correspondence. Our results also give new connections between a surface cusp singularity, its dual and hyperbolic Inoue surfaces. version 2: References added.