The virtual Poincare polynomials of homogeneous spaces

Details The virtual Poincare polynomials of homogeneous spaces The virtual Poincare polynomials of homogeneous spaces

2001-02-07

arxiv.org/abs/math/0102052v1

Mathematics

Algebraic Geometry

LaTeX, 14 pages

Scientific paper

We factor the virtual Poincare polynomial of every homogeneous space G/H, where G is a complex connected linear algebraic group and H is an algebraic subgroup, as $t^{2u} (t^2-1)^r Q_{G/H}(t^2)$ for a polynomial $Q_{G/H}$ with non-negative integer coefficients. Moreover, we show that $Q_{G/H}(t^2)$ divides the virtual Poincar\'e polynomial of every regular embedding of G/H, if H is connected.

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