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- Title
Minimal Free Resolutions of Zero-dimensional Schemes in ℙ<sup>1</sup> × ℙ<sup>1</sup>.
- Authors
Bonacini, Paola; Marino, Lucia
- Abstract
Let X be a zero-dimensional scheme in ℙ1 × 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 depend 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.
- Subjects
FREE resolutions (Algebra); DIMENSIONAL analysis; SCHEMES (Algebraic geometry); SET theory; HILBERT functions
- Publication
Algebra Colloquium, 2015, Vol 22, Issue 1, p97
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386715000097