2008/09/17 by Wenchuan Hu, Hu, Wenchuan · 1 citation
Computer Science · Mathematics · #14C05 #14F20 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Calabi–Yau manifold #FOS: Mathematics #Generalization #K-Theory and Homology (math.KT) #Mathematical analysis #Mathematical economics #Mathematics #Mathematics and Applications #Polynomial and algebraic computation #Pure mathematics #math.AG #math.KT #msc:14C05 #msc:14F20
paper · pdf · doi:10.48550/arxiv.0809.2988
11 pages, added sections on the case by finite group actions; typos corrected
openalex publication_date 2008/09/17 · arxiv created 2008/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Euler characteristic of Chow varieties of algebraic cycles of a given degree in complex projective spaces was computed by Blaine Lawson and Stephen Yau by using holomorphic symmetries of cycles spaces. In this paper we compute this in a direct and elementary way and generalize this formula to the l-adic Euler-Poincare characteristic for Chow varieties over any algebraically closed field. Moreover, the Euler characteristic for Chow varieties with certain group action is calculated. In particular, we calculate the Euler characteristic of the space of right quaternionic cycles of a given dimension and degree in complex projective spaces.