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

Abstract

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 by
k[x,y]
(f)
and m a maximal ideal of R. Assume that Rm, the localization
of R at m, is not a regular ring. Let Ω2(Rm) be the universal module
of 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 rings
R.

Keywords

• Universal module,Universal differential operators,Betti series,Minimal resolution

References

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