Kähler differential algebras for 0-dimensional schemes

Given a 0-dimensional scheme X in a projective n-space Pn over a field K, we study the Kähler differential algebra ΩRX/K of its homogeneous coordinate ring RX. Using explicit presentations of the modules ΩRX/Km of Kähler differential m-forms, we determine many values of their Hilbert functions explicitly and bound their Hilbert polynomials and regularity indices. Detailed results are obtained for subschemes of P1, fat point schemes, and subschemes of P2 supported on a conic.