A Structure Theorem and the Graded Betti Numbers for Almost Complete Intersections

Details A Structure Theorem and the Graded Betti Numbers for Almost Complete Intersections A Structure Theorem and the Graded Betti Numbers for Almost Complete Intersections

2010-02-16

arxiv.org/abs/1002.3026v1

Mathematics

Algebraic Geometry

Scientific paper

We provide a structure theorem for all almost complete intersection ideals of depth three in any Noetherian local ring. In particular, we find that the minimal generators are the pfaffians of suitable submatrices of an alternating matrix. From the graded version of the previous result, we characterize the graded Betti numbers of all 3-codimensional almost complete intersection schemes of P^r.

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