Arc spaces of cA-type singularities

2013/06/05 by Johnson, Jennifer M., Kollár, János · 1 citation
#14B05 (Primary) 14J17 #14E15 #14E18 #32S05 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1306.1208

Abstract

We study the space of arcs on a singularity of the form xy=f(z₁,..., z_n) and prove 2 main results. (i) The number of irreducible components equals the multiplicity of f minus 1. (ii) If n>1 and the leading homogeneous term of f is not a perfect square then the Nash map from the set of irreducible components to the set of essential divisors is not surjective.

Cited by

• On the Nash Problem over 3-Fold Terminal Singularities of Type cAx/2

Related

• Arc spaces of cA₁ singularities
• The Nash problem on arc families of singularities
• The space of arcs of an algebraic variety
• Contact loci in arc spaces
• The Nash problem of arcs and the rational double point E₆