parameterized algorithms for geometric set cover Are there any parametrized algorithms $W$-hardness results known for the computational problem Geometric Set Cover?

It is known that set cover problem is $W[2]$ hard when parametrized by the solution size? There might be some advantages when the sets are defined by geometric objects.
The paper D. Marx: Efficient approximation schemes for geometric problems?, in ESA 2005, gives W1-hardness for covering points with unit squares. A draft is here.