Rationality criteria for motivic zeta-functions

Preprint

11 December 2002

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0212158

Abstract

The zeta-function of a complex variety is a power series whose nth coefficient is the nth symmetric power of the variety, viewed as an element in the Grothendieck ring of complex varieties. We prove that the zeta-function of a surface is rational if and only if its Kodaira dimension is negative.

Keywords

FUNCTION OF A SURFACE
RATIONALITY CRITERIA
NTH COEFFICIENT
COMPLEX VARIETY
ZETA FUNCTION
MOTIVIC ZETA

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