On t-equivariant rational equivalence of t-equivariant cycles

Abstract EN

Let Pm be the m-dimensional projective space over the field of complex numbers C acted on by the algebraic torus T = (C*) m + 1 .

Let X be an equivariantly embedded variety in Pm via the map φ, i.

e., φ is an embedding and t.

φ (x) € φ (X) whenever t € T and x € X .

We begin a study of T-equivariant rational equivalence of T-equivariant cycles on a B-variety X, namely a non-singular projective variety with an action of a torus T = (C*) m+1with many fixed points.

First, we compute the T-equivariant Picard group of such a variety with the help of fixed point and their associated characters.

This result is then applied to study more generally Tequivariant rational equivalence of T-equivariant cycles.