The Dynkin-range licci conjecture for perfect ideals

Let II be a grade cc perfect ideal in a local Noetherian ring RR. Let dd denote the deviation of II and tt the minimal number of generators of Extc(R/I,R)\operatorname{Ext}^c(R/I,R). Let Tc1,d+1,t+1T_{c-1,d+1,t+1} be the indicated diagram. Dynkin-range licci conjecture. If Tc1,d+1,t+1T_{c-1,d+1,t+1} is a Dynkin diagram, equivalently if

1c1+1d+1+1t+1>1,\frac{1}{c-1}+\frac{1}{d+1}+\frac{1}{t+1}>1,

then II is in the linkage class of a complete intersection. This extends the theorem proved in the paper within the stated Dynkin range; outside that range, examples show that perfect ideals with the same Betti numbers need not be licci.

Sources & referencesView supporting material

Primary source

Lorenzo Guerrieri, Xianglong Ni and Jerzy Weyman, “An ADE correspondence for grade three perfect ideals”, arXiv:2407.02380 (2024).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.