2009/12/03 by Wenchuan Hu, Hu, Wenchuan
Computer Science · Mathematics · #14C05 #14C25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14C05 #msc:14C25
paper · pdf · doi:10.48550/arxiv.0912.0563
16 pages, Title changed, more additive invariants are considered
openalex publication_date 2009/12/03 · arxiv created 2010/10/26 · arxiv updated 2010/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The additive invariants of an algebraic variety is calculated in terms of those of the fixed point set under the action of additive and multiplicative groups, by using Bialynicki-Birula's fixed point formula for a projective algebraicset with a Gm-action or Ga-action. The method is also generalized to calculate certain additive invariants for Chow varieties. As applications, we obtain 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-Poincare characteristic for the Chow varieties of certain projective varieties over an algebraically closed field of arbitrary characteristic. Moreover, we show that the virtual Hodge (p,0) and (0,q)-numbers of the Chow varieties and affine group varieties are zero for all p,q positive.