Symbolic analytic spread: upper bounds and applications

Abstract

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.

to appear in J. Inst. Math. Jussieu

References in corpus (3)

• A Zariski-Nagata theorem for smooth $\mathbb{Z}$-algebras
• Local cohomology bounds and test ideals
• Symbolic and Ordinary Powers of Ideals in Hibi Rings

Cited by in corpus (1)

• Symbolic powers of determinantal ideals in prime characteristic