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.
Favacchio G., Guardo E. (2019). On the Betti numbers of three fat points in P1 × P1. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 56(3), 751-766 [10.4134/JKMS.j180385].
On the Betti numbers of three fat points in P1 × P1
Favacchio G.;
2019-01-01
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.File | Dimensione | Formato | |
---|---|---|---|
FG-postprint editorial -korean.pdf
Solo gestori archvio
Descrizione: Articolo principale
Tipologia:
Versione Editoriale
Dimensione
350.04 kB
Formato
Adobe PDF
|
350.04 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.