6533b7d6fe1ef96bd1266d89
RESEARCH PRODUCT
On the Betti numbers of three fat points in P1 × P1
Giuseppe FavacchioElena Maria Guardosubject
13F20Fat points Hilbert functions Multiprojective spaces13A15Fat pointsMathematics - Commutative Algebra13D40Mathematics - Algebraic GeometrySettore MAT/02 - AlgebraFat points; Hilbert functions; Multiprojective spacesMultiprojective spacesSettore MAT/03 - GeometriaMathematics - Algebraic Geometry; Mathematics - Algebraic Geometry; Mathematics - Commutative Algebra; 13F20 13A15 13D40 14M0514M05Hilbert functionsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-01-01 |