2020/09/08 by Chen, Bingyi
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2009.03613
Fix a subset I⊆ \mathbb R>0 such that γ=inf\ ∑inibi-1>0 | ni∈ \mathbb Z≥ 0, bi∈ I \>0. We give a explicit upper bound ℓ(γ)∈ O(1/γ2) as γ→ 0, such that for any smooth surface A of arbitrary characteristic with a closed point 0 and an \mathbb R-ideal \mathfraka with exponents in I, there always exists a prime divisor E over A computing the minimal log discrepancy of (A,\mathfraka) at 0 and with its log discrepancy kE+1≤ ℓ(γ). Some examples indicate that our bound is optimal.