arXiv subjects

Phan Van Thien

Publications and source records attributed to Phan Van Thien.

4 recordsLinked to original sources

arXiv2024

The regularity index, Hilbert function of fat points and the embedding

Let $m \ge n$, $ϕ_{n,m}: \mathbb P^n \to \mathbb P^m$, $ϕ_{n,m}(a_1, \ldots, a_n)=(a_1, \ldots, a_n, 0, \ldots, 0)$, be the embedding, $Z=m_1P_1+\cdots+m_sP_s$ be fat points in $\mathbb P^n$ and $ϕ_{n,m}(Z)=m_1ϕ_{n,m}(P_1)+\cdots+m_sϕ_{n,m}(P_s)$ be fat points in $\mathbb P^m$. We show the relation between the regularity index, Hilbert function of the fat points $Z$ and the regularity index, Hilbert function of the fat points $ϕ_{n,m}(Z)$.

math.AG↗

arXiv2022

On invariant of the regularity index of fat points

We prove invariant of the regularity index of fat points under changes of the linear subspace containing the support of the fat points. Then we show that Segre's bound is attained by any set of s non-degenerate equimultiple fat points in $\mathbb P^n$, $s\le n+3$. We also give an example showing that there always exists a set of n+4 non-degenerate equimultiple fat points in $\mathbb P^n$ such that Segre's bound is not attained.

math.AG↗

arXiv2016

Lower bound for the regularity index of fat points

The problem to find an upper bound for the regularity index of fat points has been dealt with by many authors. In this paper we give a lower bound for the regularity index of fat points. It is useful for determining the regularity index.

math.AC↗

arXiv2016

On the regularity index of $s$ equimultiple fat points not on a linear $(r-1)$-space, $s \le r+3$

We prove the Trung's conjecture about Segre's upper bound for s equimultiple fat points not on a linear (r-1)-space, s\le r+3, by algebraic method used in [3]. This method also may used to research other cases of fat points.

math.AC↗