RESULTS ON BETTI SERIES OF THE UNIVERSAL MODULES OF SECOND ORDER DERIVATIONS

Abstract

Let R be the coordinate ring of an affine irreducible curve presented byk[x,y](f)and m a maximal ideal of R. Assume that Rm, the localizationof R at m, is not a regular ring. Let Ω2(Rm) be the universal moduleof second order derivations of Rm. We show that, under certain conditions, B(Ω2(Rm), t), the Betti series of Ω2(Rm), is a rational function.To conclude, we give examples related to B(Ω2(Rm), t) for various ringsR.