Arc spaces of cA-type singularities
Abstract
We study the space of arcs on a singularity of the form xy=f(z1,..., zn) 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.
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