Let X be a zero-dimensional scheme in P 1 × P 1 . 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.

Minimal free resolutions of 0-dimensional schemes in P1xP1

BONACINI, PAOLA;MARINO, LUCIA MARIA
2015

Abstract

Let X be a zero-dimensional scheme in P 1 × P 1 . 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.
resolution, Hilbert function, separators
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/246659
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