Motivic integrals and functional equations
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E. Gorskiĭ
Translated by: the author - St. Petersburg Math. J. 19 (2008), 561-575
- DOI: https://doi.org/10.1090/S1061-0022-08-01010-8
- Published electronically: May 9, 2008
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Abstract:
A functional equation for the motivic integral corresponding to the Milnor number of an arc is derived by using the Denef–Loeser formula for the change of variables. Its solution is a function of five auxiliary parameters, it is unique up to multiplication by a constant, and there is a simple recursive algorithm to find its coefficients. The method is fairly universal and gives, for example, equations for the integral corresponding to the intersection number over the space of pairs of arcs and over the space of unordered collections of arcs.References
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Bibliographic Information
- E. Gorskiĭ
- Affiliation: Moscow State University and Independent University of Moscow, Russia
- Email: gorsky@mccme.ru
- Received by editor(s): October 3, 2006
- Published electronically: May 9, 2008
- Additional Notes: Supported by the grant NSh-4719.2006.1
- © Copyright 2008 American Mathematical Society
- Journal: St. Petersburg Math. J. 19 (2008), 561-575
- MSC (2000): Primary 32S45, 28B10
- DOI: https://doi.org/10.1090/S1061-0022-08-01010-8
- MathSciNet review: 2381934