Resolutions that arise as iterated mapping cones are considered. Explicit resolutions are given for monomial ideals with linear quotients which admit decomposition functions, and it is studied under which conditions a mapping cone admits a DG algebra structure.

Algebraic and combinatorial properties of a monomial ideal and its radical are compared.

Abstract. We introduce a class of Stanley-Reisner ideals called a generalized complete intersection, which is characterized by the property that all the residue class rings of powers of the ideal have FLC. We also give a combinatorial characterization of such ideals.

a b s t r a c tWe consider a family of slightly extended version of Raynaud's surfaces X over the field of positive characteristic with Mumford-Szpiro type polarizations Z, which have Kodaira non-vanishing H 1 (X, Z −n ) = 0 for all 1 ≤ n ≤ N with some N ≥ 1. The surfaces are at least normal but smooth under a special condition. We also give a fairly large family of non-Mumford-Szpiro type polarizations Z a,b with Kodaira non-vanishing.

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