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MOTIVIC HILBERT ZETA FUNCTIONS OF CURVES ARE RATIONAL

Published online by Cambridge University Press:  31 October 2018

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)

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.

Type
Research Article
Copyright
© Cambridge University Press 2018

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