On the Cohen-Macaulay type of s-lines in An + 1

AbstractLet A be the coordinate ring of s-lines through the origin in An + 1(k). We discuss what it means for these lines to be in “sufficiently general position” and then, with this restriction on the lines, we attempt to verify our belief that the Cohen-Macaulay type of A depends only on s and n. We characterize those s and n for which A is a Gorenstein ring (i.e. of C-M type 1) and explicitly calculate the Cohen-Macaulay type in several other cases. We then extend some of our results to the case of an arbitrary reduced curve whose tangent cone consists of lines in sufficiently general position. Finally, we calculate the Hubert-Samuel polynomials of the curves we have been considering