Hilbert functions of schemes of double and reduced points

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Carlini, Enrico¹  Catalisano, Maria Virginia²  Guardo, Elena³  Van Tuyl, Adam⁴ 

[1] Politecn Torino, Dept Math Sci, DISMA, Turin, Italy

[2] Univ Genoa, Dipartimento Ingn Meccan Energet Gest & Trasporti, Genoa, Italy

[3] Univ Catania, Dipartimento Matemat & Informat, Viale A Doria 6, I-95100 Catania, Italy

[4] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4L8, Canada

关键词: Fat points;    Star configuration points;    Hilbert functions;   

DOI  :  10.1016/j.jpaa.2019.07.009

来源: Elsevier

【 摘 要 】

It remains an open problem to classify the Hilbert functions of double points in P-2. Given a valid Hilbert function H of a zero-dimensional scheme in P-2, we show how to construct a set of fat points Z subset of P-2 of double and reduced points such that H-Z, the Hilbert function of Z, is the same as H. In other words, we show that any valid Hilbert function H of a zero-dimensional scheme is the Hilbert function of a set a positive number of double points and some reduced points. For some families of valid Hilbert functions, we are also able to show that H is the Hilbert function of only double points. In addition, we give necessary and sufficient conditions for the Hilbert function of a scheme of a double points, or double points plus one additional reduced point, to be the Hilbert function of points with support on a star configuration of lines. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free