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Journal of the Ramanujan Mathematical Society

Volume 28A, Issue SPL, July – Special Issue 2013  pp. 247–266.

Are symbolic powers highly evolved?

Authors Brian Harbourne and Craig Huneke
Author institution: Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130, USA

Summary:  Searching for structural reasons behind old results and conjectures of Chudnovksy regarding the least degree of a nonzero form in an ideal of fat points in N, we make conjectures which explain them, and we prove the conjectures in certain cases, including the case of general points in 2. Our conjectures were also partly motivated by the Eisenbud-Mazur Conjecture on evolutions, which concerns symbolic squares of prime ideals in local rings, but in contrast we consider higher symbolic powers of homogeneous ideals in polynomial rings.

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