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arXiv · 0907.0953

On some moduli spaces of bundles on K3 surfaces, II

C. G. Madonna
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Abstract

We give many examples in which there exist 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 $rk N(S)=ρ(S)=2$ 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 lenght equal to $g-rs$. This result generalizes the main result of \cite{Nik1} when $g=rs+1$ and of \cite{Monat} when $r=s=2$, $g \geq 5$.

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C. G. Madonna. 2010-08-15. On some moduli spaces of bundles on K3 surfaces, II. https://arxiv.org/abs/0907.0953

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