Physical Sciences and Mathematics Commons^™

Are Symbolic Powers Highly Evolved?, Brian Harbourne, Craig Hunkeke

Department of Mathematics: Faculty Publications

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 PN, we make conjectures which explain them, and we prove the conjectures in certain cases, including the case of general points in P2. 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.