Jet schemes and invariant theory

Details Jet schemes and invariant theory Jet schemes and invariant theory

2011-12-29

arxiv.org/abs/1112.6230v1

Mathematics

Algebraic Geometry

This paper corrects the error in Theorem 5.3 of arXiv:0807.4764. This theorem is false in general, but it holds in the cases w

Scientific paper

Given a complex, reductive algebraic group G and a G-module V, the mth jet scheme G_m acts on the mth jet scheme V_m for all m\geq 1. There is a natural map O((V//G)_m) --> O(V_m)^{G_m} which in general fails to be an isomorphism. Under some conditions a stabilization phenomenon occurs at the level of arc spaces, and the induced map O((V//G)_{\infty}) --> O(V_{\infty})^{G_{\infty}} is an isomorphism. We give a sufficient criterion for this to occur, and prove that it holds when G=SL_n, GL_n, SO_n, or Sp_{2n} and V is a sum of copies of the standard representation and its dual.

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