Are symbolic powers highly evolved?

Details Are symbolic powers highly evolved? Are symbolic powers highly evolved?

2011-03-30

arxiv.org/abs/1103.5809v3

Mathematics

Commutative Algebra

13 pages; for version 3 a minor change was made to the acknowledgments but no change was made to mathematical content; for ver

Scientific paper

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 projective N-space, we make conjectures which explain them, and we prove the conjectures in certain cases, including the case of general points in the projective plane. 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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