Minimal Free Resolutions of 0-Dimensional Schemes in P1 \times P1

Details Minimal Free Resolutions of 0-Dimensional Schemes in P1 \times P1 Minimal Free Resolutions of 0-Dimensional Schemes in P1 \times P1

2011-08-19

arxiv.org/abs/1108.4007v1

Mathematics

Algebraic Geometry

Scientific paper

Let X be a zero-dimensional scheme in P1 \times P1. Then X has a minimal free resolution of length 2 if and only if X is ACM. In this paper we determine a class of reduced schemes whose resolutions, similarly to the ACM case, can be obtained by their Hilbert functions and depends only on their distributions of points in a grid of lines. Moreover, a minimal set of generators of the ideal of these schemes is given by curves split into the union of lines.

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