## Intersection theory on spherical varieties.(English)Zbl 0819.14019

Spherical varieties are varieties with reductive group actions containing dense orbits of Borel subgroups; there are many important examples including all flag manifolds and toric varieties. This paper gives a finite presentation for the Chow homology groups of any variety $$X$$ on which a connected solvable linear algebraic group (for example a Borel subgroup of a reductive group) acts with only finitely many orbits. The authors show that the Künneth map $A_ * (X) \otimes A_ * (Y) \to A_ * (X \times Y)$ is then an isomorphism for any scheme $$Y$$. In addition if $$X$$ is complete they give a method to compute the operational Chow cohomology groups of $$X$$ (the Kronecker duality map is shown to be an isomorphism).
Reviewer: F.Kirwan (Oxford)

### MSC:

 14L30 Group actions on varieties or schemes (quotients) 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 20G10 Cohomology theory for linear algebraic groups