EXTENSION GROUPS OF TAUTOLOGICAL SHEAVES ON HILBERT SCHEMES

We give formulas for the extension groups between tautological sheaves and more generally between tautological objects twisted by natural line bundles on the Hilbert scheme of points on a smooth quasi-projective surface. As a consequence we observe that a tautological object can never be a spherical or P-n-object. We also provide a description of the Yoneda products.