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Integration over a space of non-parametrized arcs, and motivic analogues of the monodromy zeta function

Melle Hernández, Alejandro and Gusein-Zade, Sabir Medgidovich and Luengo Velasco, Ignacio (2006) Integration over a space of non-parametrized arcs, and motivic analogues of the monodromy zeta function. Proceedings of the Steklov Institute of Mathematics, 252 (1). pp. 63-73. ISSN 1531-8605

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Abstract

Notions of integration of motivic type over the space of arcs factorized by the natural C*-action and over the space of nonparametrized arcs (branches) are developed. As an application, two motivic versions of the zeta function of the classical monodromy transformation of a germ of an analytic function on ℂd are given that correspond to these notions. Another key ingredient in the construction of these motivic versions of the zeta function is the use of the so-called power structure over the Grothendieck ring of varieties introduced by the authors.


Item Type:Article
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:13920
Deposited On:18 Nov 2011 08:20
Last Modified:06 Feb 2014 09:55

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