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arXiv · 1306.1208

Arc spaces of cA-type singularities

Jennifer M. Johnson·János Kollár
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Abstract

We study the space of arcs on a singularity of the form xy=f(z_1,..., 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.

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Jennifer M. Johnson, János Kollár. 2013-06-05. Arc spaces of cA-type singularities. https://arxiv.org/abs/1306.1208

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