Ideals of Powers and Powers of Ideals by Enrico Carlini & Huy Tài Hà & Brian Harbourne & Adam Van Tuyl

Author:Enrico Carlini & Huy Tài Hà & Brian Harbourne & Adam Van Tuyl
Language: eng
Format: epub
ISBN: 9783030452476
Publisher: Springer International Publishing

holds for each r > 1.

It turns out the containment I((Nr − N + 1)Z) ⊆ I(Z)r often holds, but not always. The first failure of containment was given by Dumnicki, Szemberg, and Tutaj-Gasińska [58], for which the ground field was the complex numbers and N = r = 2. Additional failures are given by Dumnicki et al. [59], but so far no failures over the complex numbers are known if either r > 2 or N > 2. This suggests that perhaps the following problem at least has an affirmative answer, but this problem remains open.

Question 9.7

Let be a fat point subscheme. Then is it always true that

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