Physical Sciences and Mathematics Commons^™

Comparing Powers Of Edge Ideals, Mike Janssen, Thomas Kamp, Jason Vander Woude

Faculty Work Comprehensive List

Given a nontrivial homogeneous ideal I ⊆ k[x1, x2, . . . ,xd], a problem of great recent interest has been the comparison of the rth ordinary power of I and the mth symbolic power I(m). This comparison has been undertaken directly via an exploration of which exponents m and r guarantee the subset containment I(m) ⊆ Ir and asymptotically via a computation of the resurgence ρ(I), a number for which any m/r > ρ(I) guarantees I(m) ⊆ Ir. Recently, a third quantity, the symbolic defect, was introduced; as It ⊆ I(t), the symbolic defect is the minimal number of generators …