论文标题
上限的理想和算术程度的自由基的规律性
Upper bounds for regularity of radicals of ideals and arithmetic degrees
论文作者
论文摘要
令$ s $为$ n $变量的多项式戒指。让$ i $是由$ \ d $带有$ \ text {dim}（s/i）= r $的$ d $生成的$ s $的同质理想。在本文的第一部分中，我们展示了如何从HOA的结果中获得$ \ sqrt {i} $的规律性。更具体地说，我们表明$ \ text {reg}（\ sqrt {i}）\ leq d^{（n-1）2^{r-1}} $。在第二部分中，我们表明$ r $ th的$ i $的算术度在上面的$ 2 \ cdot d^{2^{n-r-1}} $。这是通过证明强烈稳定理想和Borel类型理想的算术程度的上限来完成的。
Let $S$ be a polynomial ring in $n$ variables over a field. Let $I$ be a homogeneous ideal in $S$ generated by forms of degree at most $d$ with $\text{dim}(S/I)=r$. In the first part of this paper, we show how to derive from a result of Hoa an upper bound for the regularity of $\sqrt{I}$. More specifically we show that $\text{reg}(\sqrt{I})\leq d^{(n-1)2^{r-1}}$. In the second part, we show that the $r$-th arithmetic degree of $I$ is bounded above by $2\cdot d^{2^{n-r-1}}$. This is done by proving upper bounds for arithmetic degrees of strongly stable ideals and ideals of Borel type.
