Asymptotic resurgences for ideals of positive dimensional subschemes of projective space

By Elena Guardo, Brian Harbourne, Adam Van Tuyl. 2012

84 citations recorded by the source corpus.

Recent work of Ein-Lazarsfeld-Smith and Hochster-Huneke raised the problem of determining which symbolic powers of an ideal are contained in a given ordinary power of the ideal. Bocci-Harbourne defined a quantity called the resurgence to address this problem for homogeneous ideals in polynomial rings, with a focus on zero dimensional subschemes of projective space; the methods and results obtained there have much less to say about higher dimensional subschemes. Here we take the first steps toward extending this work to higher dimensional subschemes. We introduce new asymptotic versions of the resurgence and obtain upper and lower bounds on them for ideals of smooth subschemes, generalizing what is done by Bocci-Harbourne. We apply these bounds to ideals of unions of general lines in ${\bf P}^N$. We also pose a Nagata type conjecture for symbolic powers of ideals of lines in ${\bf P}^3$.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/47e91151931e7c36c2e6c277fbb735c1b89233d5

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Matroid configurations and symbolic powers of their ideals (2015, background): “This limit is known to exist and in various situations it is of interest to compute it or at least to estimate it ([5, 18, 12]).”
The Waldschmidt constant for squarefree monomial ideals (2015, background): “Van Tuyl acknowledges the financial support provided by NSERC.”