The Lawson-Yau Formula and its generalization

Details The Lawson-Yau Formula and its generalization The Lawson-Yau Formula and its generalization

2008-09-17

arxiv.org/abs/0809.2988v2

Mathematics

Algebraic Geometry

11 pages, added sections on the case by finite group actions; typos corrected

Scientific paper

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.

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