Mustaţă's ideal-adic semi-continuity conjecture for minimal log discrepancies of pairs

Let (X,Δ)(X,\Delta) be a pair, meaning that XX is a normal variety and Δ\Delta is an effective R\mathbb{R}-divisor with KX+ΔK_X+\Delta an R\mathbb{R}-Cartier divisor. Let ZZ be a closed subset of XX, and let a\mathfrak{a} and b\mathfrak{b} be R\mathbb{R}-ideal sheaves. Write alb\mathfrak{a}\sim_l\mathfrak{b} for the ideal-adic equivalence used in the source. Mustaţă's conjecture. There exists a real number ll such that, whenever alb\mathfrak{a}\sim_l\mathfrak{b},

mldZ(X,Δ,a)=mldZ(X,Δ,b).\operatorname{mld}_Z(X,\Delta,\mathfrak{a})=\operatorname{mld}_Z(X,\Delta,\mathfrak{b}).

This is the direct extension proposed in the source of ideal-adic semi-continuity for log canonicity to minimal log discrepancies; its resolution status is not given.

Sources & referencesView supporting material

Primary source

Masayuki Kawakita, “Ideal-adic semi-continuity problem for minimal log discrepancies”, arXiv:1012.0395 (2010).

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.