On the Fluctuations in Colon Powers of Monomial Ideals

par Mehrdad Nasernejad

mardi 27 oct. 2026, 14:00 → 15:30 Europe/Paris

S3 351 (Sciences 3)

Let I be an ideal in a commutative Noetherian ring R. We introduce the notion of fluctuation in colon powers if there exist positive integers a < b < c such that at least one of the following cases occurs :
(i) (I^a : I) = I^a−1, (I^b : I) ≠ I^b−1, but (I^c : I) = I^c−1.
(ii) (I^a : I) ≠ I^a−1, (I^b : I) = I^b−1, but (I^c : I) ≠ I^c−1.
In this talk, we are going to explore this phenomenon for monomial ideals.

Source:
M. Nasernejad and J. Toledo, Strong persistence index and fluctuations in colon powers of monomial ideals, Mathematics 2026, 14(10), 1705.
doi:https://doi.org/10.3390/math14101705