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All symbolic powers and ordinary powers of the defining ideal of a fat nearly-complete intersection are equal

Hassan Haghighi

Mathematics Faculty, K. N. Toosi University of Technology, Tehran, Iran

E-mail Address: haghighi@kntu.ac.ir

Corresponding author.

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and

Mohammad Mosakhani

Mathematics Faculty, K. N. Toosi University of Technology, Tehran, Iran

E-mail Address: mosakhani@aut.ac.ir

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https://doi.org/10.1142/S0219498819501421Cited by:1 (Source: Crossref)

Abstract

The purpose of this paper is to study the containment problem for the corresponding ideal $I_{Z}$ of a special zero dimensional subscheme $Z$ in $ℙ^{2}$ , what we call a fat nearly-complete intersection. We show that for every positive integer $m$ , the equality $I_{Z}^{(m)} = I_{Z}^{m}$ holds.

Communicated by T. H. Ha

Keywords:

AMSC: 14N20, 13A15, 14N05, 13F20

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