Montaldi, James and van Straten, Duco
(1993)
*Quotient spaces and critical points of invariant functions
for C*-actions.*
J. reine angew. Math., 437.
pp. 55-99.
ISSN 0075-4102

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## Abstract

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 differential forms for such an action, and use these to define an algebraic notion of multiplicity for critical points of functions which are invariant under the C∗-action. We also prove a theorem relating the cohomology of the Milnor fibre of the critical point on the quotient space with this algebraic multiplicity. We also include an appendix showing how to use Cech complexes to compute local cohomology.

Item Type: | Article |
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Uncontrolled Keywords: | Group actions, local cohomology, invariant functions, critical points |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry MSC 2010, the AMS's Mathematics Subject Classification > 32 Several complex variables and analytic spaces |

Depositing User: | Dr James Montaldi |

Date Deposited: | 04 Nov 2008 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1065 |

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