论文标题
主要特征中决定性理想的符号能力
Symbolic powers of determinantal ideals in prime characteristic
论文作者
论文摘要
我们研究了具有主要特征的普通矩阵的通用，对称和汉克尔矩阵的确定性理想的符号能力。具体而言，我们表明限制$ \ lim \ limits_ {n \ to \ infty} \ frac {\ textrm {reg}（i^{（n）}）} {n} $存在，并且存在$ \ textrm {depth}（depth}（depth}（r/i^{（n）} {（n）} $ nizes $ nibes $此外，我们为$ \ textrm {depth}（r/i^{（n）}）$的稳定值提供明确的公式。为了展示这些结果，我们介绍了符号$ f $ p $ - 理想的概念，这对上述理想所满足。此外，我们发现符号$ f $ - 纯理想所满足的几个属性。例如，我们表明他们的象征性REES代数和符号相关的分级代数为$ f $ pure。结果，他们的$ $ invariants和深度呈现出良好的行为。此外，我们还为符号$ f $ purity提供了类似Fedder的标准。
We study the symbolic powers of determinantal ideals of generic, generic symmetric, and Hankel matrices of variables, and of Pfaffians of generic skew-symmetric matrices, in prime characteristic. Specifically, we show that the limit $\lim\limits_{n\to\infty} \frac{\textrm{reg}(I^{(n)})}{n}$ exists and that $\textrm{depth}(R/I^{(n)})$ stabilizes for $n\gg 0$. Furthermore, we give explicit formulas for the stable value of $\textrm{depth}(R/I^{(n)})$ in the generic and skew-symmetric cases. In order to show these results, we introduce the notion of symbolic $F$-purity of ideals which is satisfied by the classes of ideals mentioned above. Moreover, we find several properties satisfied by symbolic $F$-pure ideals. For example, we show that their symbolic Rees algebras and symbolic associated graded algebras are $F$-pure. As a consequence, their $a$-invariants and depths present good behaviors. In addition, we provide a Fedder's-like Criterion for symbolic $F$-purity.
