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MOTIVIC HILBERT ZETA FUNCTIONS OF CURVES ARE RATIONAL

Part of: Cycles and subschemes Curves Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  31 October 2018

Dori Bejleri ,
Dhruv Ranganathan  and
Ravi Vakil
Dori Bejleri
Affiliation:
Department of Mathematics, Brown University, Providence RI 02913, USA (dbejleri@math.brown.edu)
Dhruv Ranganathan
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02138, USA (dhruvr@mit.edu)
Ravi Vakil
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, USA (vakil@math.stanford.edu)
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Abstract

The motivic Hilbert zeta function of a variety $X$ is the generating function for classes in the Grothendieck ring of varieties of Hilbert schemes of points on $X$. In this paper, the motivic Hilbert zeta function of a reduced curve is shown to be rational.

Keywords

Hilbert schemeszeta functionscurve singularities

MSC classification

Primary: 14C05: Parametrization (Chow and Hilbert schemes) 14H20: Singularities, local rings 14G10: Zeta-functions and related questions (Birch-Swinnerton-Dyer conjecture)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 3 , May 2020 , pp. 947 - 964
Copyright
© Cambridge University Press 2018

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