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On Additive invariants of actions of additive and multiplicative groups

Published online by Cambridge University Press:  01 May 2013

Wenchuan Hu
Wenchuan Hu*
Affiliation:
School of Mathematics, Sichuan University, Chengdu 610064, P. R. Chinahuwenchuan@gmail.com
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Abstract

Let X be an algebraic variety with an action of either the additive or multiplicative group. We calculate the additive invariants of X in terms of the additive invariants of the fixed point set, using a formula of Białynicki-Birula. The method is also generalized to calculate certain additive invariants for Chow varieties. As applications, we obtain results on the Hodge polynomial of Chow varieties in characteristic zero and the number of points for Chow varieties over finite fields. As applications, we obtain the l-adic Euler-Poincaré characteristic for the Chow varieties of certain projective varieties over a field of arbitrary characteristic. Moreover, we show that the virtual Hodge (p,0) and (0,q)-numbers of the Chow varieties and affine algebraic group varieties are zero for all p,q positive.

Keywords

Additive invariantsgroup actionsvirtual Hodge numbersChow variety14L3014C05
Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 3 , December 2013 , pp. 551 - 568
Copyright
Copyright © ISOPP 2013 

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