ar X iv : a lg - g eo m / 9 61 00 12 v 1 1 1 O ct 1 99 6 MONOMIAL RESOLUTIONS
نویسندگان
چکیده
Let M be a monomial ideal in the polynomial ring S = k[x1, . . . , xn] over a field k. We are interested in the problem of resolving S/M over S. The difficulty in resolving minimally is reflected in the fact that the homology of arbitrary simplicial complexes can be encoded (via the Stanley-Reisner correspondence) into the multigraded Betti numbers of S/M , [St]. In particular, the minimal free resolution may depend on the characteristic of k. In the study of monomial resolutions the following main directions have been pursued: construction of the minimal free resolution for special types of ideals [EK], construction of structured non-minimal resolutions [Ly], bounds for the numerical invariants of the minimal free resolution [Bi,Hu], algorithms and software for computing resolutions and Hilbert functions [BS]. We present an approach for resolving S/M by encoding the entire resolution into a single simplicial complex; the obtained resolution is minimal generically.
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