In these notes we introduce a numerical function which allows us to describe explicitly (and nonrecursively) the Betti numbers, and hence, the Hilbert function of a set Z of three fat points whose support is an almost complete intersection (ACI) in P1 × P1 . A nonrecursively formula for the Betti numbers and the Hilbert function of these configurations is hard to give even for the corresponding set of five points on a special support in P2 and we did not find any kind of this result in the literature. Moreover, we also give a criterion that allows us to characterize the Hilbert functions of these special set of fat points.

On the Betti numbers of three fat points in P1 × P1 / Favacchio, G.; Guardo, E.. - In: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY. - ISSN 0304-9914. - STAMPA. - 56:3(2019), pp. 751-766. [10.4134/JKMS.j180385]

On the Betti numbers of three fat points in P1 × P1

Favacchio G.;
2019

Abstract

In these notes we introduce a numerical function which allows us to describe explicitly (and nonrecursively) the Betti numbers, and hence, the Hilbert function of a set Z of three fat points whose support is an almost complete intersection (ACI) in P1 × P1 . A nonrecursively formula for the Betti numbers and the Hilbert function of these configurations is hard to give even for the corresponding set of five points on a special support in P2 and we did not find any kind of this result in the literature. Moreover, we also give a criterion that allows us to characterize the Hilbert functions of these special set of fat points.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2859982