On some moduli spaces of bundles on 𝐾3 surfaces, II

Madonna, C.

doi:10.1090/S0002-9939-2012-11251-1

On some moduli spaces of bundles on $K3$ surfaces, II
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Proc. Amer. Math. Soc. 140 (2012), 3397-3408 Request permission

Abstract:

We give several examples of the existence of infinitely many divisorial conditions on the moduli space of polarized $K3$ surfaces $(S,H)$ of degree $H^2=2g-2$, $g \geq 3$, and Picard number $\rho (S)=rk N(S)=2$, 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 zero-dimensional 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 $r=s=2$, $g \geq 5$.

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