Acta Mathematica Vietnamica

Acta Mathematica Vietnamica

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Regularity Index of Embedded Fat Points

Phan Van Thien , Phan Quang Nhu Anh

Abstract

Let $Z=m_1P_1+\cdots +m_sP_s$ be a set of fat points in $\mathbb{P}^n$. Let $\phi$ be a linear embedding of $\mathbb{P}^n$ in $\mathbb{P}^m,$ $ n < m$. We prove that the regularity index of $Z$ and the regularity index of $\phi(Z)$ are the same.