Algebraic rational cells and equivariant intersection theory

Abstract

Abstract. We provide a notion of algebraic rational cell with applications to intersection theory on singular varieties with torus action. Based on this notion, we study Q-filtrable varieties: algebraic varieties where a torus acts with isolated fixed points, such that the associated Bia lynicki-Birula decomposition consists of algebraic rational cells. We show that the rational equivariant Chow group of any Q-filtrable variety is freely generated by the classes of the cell closures. We apply this result to group embeddings, and more generally to spherical varieties.