# On the Hilbert function of general fat points in $\mathbb{P}^1 \times \mathbb{P}^1$

3 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , National and Kapodistrian University of Athens
Abstract : We study the bi-graded Hilbert function of ideals of general fat points with same multiplicity in $\mathbb{P}^1\times\mathbb{P}^1$. Our first tool is the multiprojective-affine-projective method introduced by the second author in previous works with A.V. Geramita and A. Gimigliano where they solved the case of double points. In this way, we compute the Hilbert function when the smallest entry of the bi-degree is at most the multiplicity of the points. Our second tool is the differential Horace method introduced by J. Alexander and A. Hirschowitz to study the Hilbert function of sets of fat points in standard projective spaces. In this way, we compute the entire bi-graded Hilbert function in the case of triple points.
Type de document :
Pré-publication, Document de travail
2017
Domaine :

Littérature citée [10 références]

https://hal.inria.fr/hal-01637942
Contributeur : Oneto Alessandro <>
Soumis le : samedi 18 novembre 2017 - 17:55:21
Dernière modification le : jeudi 11 janvier 2018 - 16:35:48

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• HAL Id : hal-01637942, version 1

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Enrico Carlini, Maria Catalisano, Alessandro Oneto. On the Hilbert function of general fat points in $\mathbb{P}^1 \times \mathbb{P}^1$. 2017. 〈hal-01637942〉

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