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The Quarterly Journal of Mathematics Advance Access published online on June 14, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han016
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© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

ETA-INVARIANTS FROM MOLIEN SERIES

Anda Degeratu{dagger}

Max Planck Institute for Gravitational Physics, Albert Einstein Institute, 14476 Golm, Germany
Duke University, Department of Mathematics, Durham, NC 27705, USA

{dagger} Corresponding author. E-mail: degeratu{at}aei.mpg.de

Received 16 November 2007; revised 13 March 2008
  Abstract

We look at the orbifold Cn/{Gamma} with {Gamma} a finite subgroup of U(n) from two perspectives: from a differential point of view it is a non-compact orbifold with boundary at infinity S2n–1/{Gamma}, while from an algebraic point of view it is a scheme with coordinate ring the {Gamma}-invariant polynomials in n variables. The main result is a relation between the {eta}-invariant of the boundary (an analytical object) and the Molien series of the singularity (an algebraic object).


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