Translator Disclaimer
August 2020 On the Hilbert Function of General Fat Points in P 1 × P 1
Enrico Carlini, Maria Virginia Catalisano, Alessandro Oneto
Michigan Math. J. 69(3): 601-632 (August 2020). DOI: 10.1307/mmj/1596700821

Abstract

We study the bi-graded Hilbert function of ideals of general fat points with same multiplicity in P 1 × 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.

Citation

Download Citation

Enrico Carlini. Maria Virginia Catalisano. Alessandro Oneto. "On the Hilbert Function of General Fat Points in P 1 × P 1 ." Michigan Math. J. 69 (3) 601 - 632, August 2020. https://doi.org/10.1307/mmj/1596700821

Information

Received: 18 July 2018; Revised: 25 September 2018; Published: August 2020
First available in Project Euclid: 6 August 2020

MathSciNet: MR4132606
Digital Object Identifier: 10.1307/mmj/1596700821

Subjects:
Primary: 14C20, 15A69
Secondary: 13A02, 13D02, 14N15

Rights: Copyright © 2020 The University of Michigan

JOURNAL ARTICLE
32 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.69 • No. 3 • August 2020
Back to Top