Quotient Spaces and Critical Points of Invariant Functions for C -actions

  title={Quotient Spaces and Critical Points of Invariant Functions for C -actions},
  author={Duco van Straten},
Consider a linear action of the group C on X = C n+1. We study the fundamental algebraic properties of the sheaves of invariant and basic diierential forms for such an action, and use these to deene an algebraic notion of multi-plicity for critical points of functions which are invariant under the C-action. We also prove a theorem relating the cohomology of the Milnor bre of the critical point on the quotient space with this algebraic multiplicity. 

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