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2008.37: Quotient spaces and critical points of invariant functions for C*-actions

2008.37: James Montaldi and Duco van Straten (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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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
Uncontrolled Keywords:Group actions, local cohomology, invariant functions, critical points
Subjects:MSC 2000 > 14 Algebraic geometry
MSC 2000 > 32 Several complex variables and analytic spaces
MIMS number:2008.37
Deposited By:Dr James Montaldi
Deposited On:04 November 2008

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