The symbolic analytic spread of an ideal $I$ is defined in terms of the rate of growth of the minimal number of generators of its symbolic powers. In this article, we find upper bounds for the symbolic analytic spread under certain conditions in terms of other invariants of $I$. Our methods also work for more general systems of ideals. As applications, we provide bounds for the (local) Kodaira dimension of divisors, the arithmetic rank, and the Frobenius complexity. We also show sufficient conditions for an ideal to be a set-theoretic complete intersection.

中文翻译：

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符号分析点差：上限和应用

理想的符号分析传播$I$是根据其象征力量的最小数量的生成者的增长率来定义的。在本文中，我们根据$I$. 我们的方法也适用于更一般的理想系统。作为应用程序，我们为除数的（本地）Kodaira 维数、算术秩和 Frobenius 复杂度提供了界限。我们还展示了理想成为集合论完全交集的充分条件。