  We prove that the homology of the Swiss-cheese operad is a Koszul operad. As
a consequence, we obtain that the spectral sequence associated to the
stratification of the compactification of points on the upper half plane
collapses at the second stage, proving a conjecture by A. Voronov. However, we
prove that the operad obtained at the second stage differs from the homology of
the Swiss-cheese operad.
