On the Betti numbers of three fat points in P1 × P1
- Autori: Favacchio G.; Guardo E.
- Anno di pubblicazione: 2019
- Tipologia: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/534021
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.