ARE SYMBOLIC POWERS HIGHLY EVOLVED

By Brian Harbourne, Craig Huneke. 2011

138 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d0d8841525b8d61aea6792274c693d1cfd8790db

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

A canonical linear system associated to adjoint divisors in characteristic $p > 0$ (2011, background): “rne observed that the characteristic p>0 result below could be easily obtained via [HH02], the simple argument is brieﬂy described in a special case in [Har09, Slide 17] and in the introduction to [HH11]. Theorem 4.9 ([Har09], cf. [EV83]). Fix a reduced closed subscheme S⊆ Pn k = X, where k is an”
On the containment problem (2016, background): “This line of investigation was suggested in [18].”
Symbolic Powers of Monomial Ideals (2013, background): “With the goal of tightening up the above containments, Harbourne and Huneke list a number of conjectured containments in [10].”