Lawson Homology for projective varieties with C^*-action

TL;DR

This paper explores how Lawson homology of smooth and certain singular projective varieties with a C^*-action can be decomposed in terms of fixed point sets, providing explicit calculations for examples.

Contribution

It establishes a decomposition formula for Lawson homology under C^*-actions and applies it to compute homology and Chow groups for specific varieties.

Findings

Lawson homology can be expressed via fixed point sets for varieties with C^*-action

Decomposition formulas extend to certain singular varieties with C^*-action

Explicit calculations of Lawson homology and higher Chow groups for examples

Abstract

The Lawson homology of a smooth projective variety with a $\C^*$-action is given in terms of that of the fixed point set of this action. We also consider such a decomposition for the Lawson homology of certain singular projective varieties with a $\C^*$-action. As applications, we calculate the Lawson homology and higher Chow groups for several examples.