We give several examples of the existence of infinitely many divisorial conditions on the moduli space of polarized K3 surfaces (S,H) of degree H ~2 = 2g - 2, g ≥ 3, and Picard number ρ(S) = rkN(S) = 2, such that for a general K3 surface S satisfying these conditions the moduli space of sheaves M _S(r,H, s) is birationally equivalent to the Hilbert scheme S[g - rs] of zerodimensional subschemes of S of length equal to g -rs. This result generalizes a result of Nikulin when g = rs + 1 and an earlier result of the author when r = s = 2, g ≥ 5.
展开▼
