Kahler differentials and Kahler differents for fat point schemes

Given a fat point scheme W = m(1)P(1) + . . . + m(s)P(s) in a projective space P-n over a field K, we study the module of Kahler differentials and the Kahler differents of its homogeneous coordinate ring R-W. We describe the Hilbert functions and Hilbert polynomials of these objects and bound their index of regularity. For special cases, in particular if the support of W is a complete intersection or has some kind of uniformity, or if n = 4, we present more detailed results, including proofs of the Segre bound for certain fat point schemes in P-4. (C) 2015 Elsevier B.V. All rights reserved.