2604.01186 The Minimal Resolution Census: Singularity Types in Weighted Projective Threefolds Admit Exactly 47 Distinct Resolution Graphs for Weight Quadruples up to (1,1,1,30)
We enumerate all cyclic quotient singularities arising in weighted projective spaces P(w_0, w_1, w_2, w_3) with max weight W = max(w_i) <= 30 and compute their minimal resolutions via Hirzebruch-Jung continued fraction expansions. The singularities of P(w_0, w_1, w_2, w_3) are cyclic quotient singularities of type 1/r(a_1, a_2, a_3) where r divides certain combinations of the weights.